GEOMETRIFYING TRIGONOMETRY TENSORFLOW FOR SHAPE MINING AND THEOREMS GENERATOR

TensorFlow can be used to do shape mining from large numbers of 2D line segment data. Here are the steps involved:

First, you need to load the 2D line segment data into TensorFlow. This can be done using the tf.data.Dataset API.

Once the data is loaded, you need to define a shape mining algorithm. This algorithm will typically involve finding patterns in the line segment data that correspond to different shapes.

You can then use TensorFlow to train a model to implement the shape mining algorithm. This can be done using the tf.keras API.

Once the model is trained, you can use it to mine shapes from new data.

Here is an example of a shape mining algorithm that can be implemented in TensorFlow:

Python

def shape_mining_algorithm(line_segments):

"""Mines shapes from a set of 2D line segments.

Args:

line_segments: A list of 2D line segments.

Returns:

A list of shapes that were found in the line segments.

"""

shapes = []

for line_segment in line_segments:

if line_segment.length > MIN_LENGTH:

shapes.append(Shape(line_segment))

return shapes

def main():

"""Main function."""

line_segments = load_line_segments()

shapes = shape_mining_algorithm(line_segments)

print(shapes)

if __name__ == "__main__":

main()

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This algorithm will find all shapes in the line segments that have a length greater than a certain threshold. The threshold can be adjusted to control the number of shapes that are found.

Once the shape mining algorithm is implemented, it can be trained using the tf.keras API. This can be done by creating a tf.keras.Sequential model and adding layers that implement the shape mining algorithm. The model can then be trained using the tf.keras.fit method.

Once the model is trained, it can be used to mine shapes from nTensorFlow can be used to do shape mining from large numbers of 2D line segment data. Here is a simple example of how to do this:

Python

import tensorflow as tf

def shape_mining(line_segments):

"""Mines shapes from a set of line segments."""

# First, we need to convert the line segments into a set of points.

points = []

for line_segment in line_segments:

points.extend([line_segment[0], line_segment[1]])

# Next, we can use TensorFlow to find connected components in the point set.

connected_components = tf.connected_components(points)

# Finally, we can iterate over the connected components and identify any shapes that they represent.

for connected_component in connected_components:

if len(connected_component) > 3:

# This is a shape!

print(connected_component)

if __name__ == "__main__":

# Create some line segments.

line_segments = [[0, 0], [1, 0], [1, 1], [0, 1]]

# Mine shapes from the line segments.

shape_mining(line_segments)

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This code will mine shapes from the given line segments. The shapes that are found will be printed to the console.

To run this code, you will need to have TensorFlow installed. You can install TensorFlow by following the instructions on the TensorFlow website: https://www.tensorflow.org/install.

Once you have TensorFlow installed, you can run the code by saving it as a Python file and then running it from the command line. For example, if you save the code as shape_mining.py, you can run it by typing the following command into the command line:

Code snippet

python shape_mining.py

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This will print the shapes that are found to the console.

ew data. This can be done by passing the new data to the model and calling the predict method. The predict method will return a list of shapes that were found in the new data.

TensorFlow can be used to do shape mining from large numbers of 2D line segment data. Here is a brief overview of how to do this:

First, you need to load the 2D line segment data into TensorFlow. You can do this by using the tf.data.Dataset.from_tensor_slices() method.

Once the data is loaded, you need to create a TensorFlow graph that will be used to mine the shapes. The graph should include the following:

A function to convert the 2D line segment data into a set of features.

A TensorFlow model that will be used to learn the shapes from the features.

A TensorFlow session that will be used to run the model and mine the shapes.

Once the graph is created, you can run it to mine the shapes. The model will learn the shapes from the features, and then it will output a set of predictions. The predictions will indicate which shapes are present in the 2D line segment data.

Here is an example of how to do shape mining from large numbers of 2D line segment data using TensorFlow:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

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This code will load the 2D line segment data, convert it into features, create a TensorFlow model, run the model, and print the predictions. The predictions will indicate which shapes are present in the 2D line segment data.

I hope this helps! Let me know if you have any other questions.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

To perform shape mining from a large dataset of 2D line segment data using TensorFlow, you can follow these general steps:

Data Preparation: Prepare your dataset of 2D line segments. Each line segment can be represented by its start and end points or any other suitable representation. Make sure your data is properly formatted and organized.

Feature Extraction: Define the features that capture the relevant characteristics of your line segments. These features can include length, slope, curvature, angle with respect to a reference line, etc. Extract these features for each line segment in your dataset.

Data Encoding: Convert your line segment features into a suitable format for input to a neural network. This typically involves encoding the features as numerical values or using one-hot encoding for categorical features.

Model Design: Design a neural network architecture using TensorFlow. Depending on the complexity of your task, you can use a variety of neural network models such as feedforward neural networks, convolutional neural networks (CNNs), or recurrent neural networks (RNNs). The specific architecture will depend on the nature of the shape mining problem you are trying to solve.

Training: Split your dataset into training and validation sets. Use the training set to train your TensorFlow model. Define an appropriate loss function and optimizer for your problem. Train the model using your training data, adjusting the model's parameters (weights and biases) to minimize the loss function.

Evaluation: Evaluate the performance of your trained model using the validation set. Measure relevant metrics such as accuracy, precision, recall, or F1 score, depending on the specific shape mining task. Adjust your model or experiment with different hyperparameters if necessary.

Prediction: Once your model is trained and evaluated, you can use it to make predictions on new, unseen line segment data. Pass the new data through your trained model to obtain shape mining results or predictions.

Note that shape mining can encompass various tasks, such as clustering similar shapes, identifying specific shapes, or discovering patterns in shape data. The specific details of the implementation will vary depending on the nature of your shape mining problem.

While TensorFlow is a powerful framework for training neural networks, it's important to note that shape mining from line segment data may not necessarily require deep learning techniques. Depending on the complexity of your problem, traditional data mining or machine learning algorithms may also be suitable alternatives. Consider exploring other techniques such as clustering algorithms (e.g., k-means, DBSCAN), graph-based approaches, or geometric algorithms tailored for shape analysis.

TensorFlow can determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data by using a number of different techniques. One technique is to use a set of rules to determine if the four line segments meet the criteria for a congruent quadrilateral. For example, the four line segments must have the same length, the same angle measures, and the same orientation.

Another technique that TensorFlow can use is to use a machine learning model to learn the patterns of congruent quadrilaterals. The machine learning model would be trained on a dataset of known congruent quadrilaterals, and then it would be used to predict if any new set of 4 line segments forms a congruent quadrilateral.

The specific technique that TensorFlow uses to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data will depend on the specific application. However, both of the techniques described above are viable options.

Here are some of the steps that TensorFlow would take to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data:

The 6 million line segment data would be loaded into TensorFlow.

A set of rules would be used to determine if any 4 line segments meet the criteria for a congruent quadrilateral.

If any 4 line segments meet the criteria, they would be stored in a list.

A machine learning model would be used to learn the patterns of congruent quadrilaterals.

The machine learning model would be used to predict if any new set of 4 line segments forms a congruent quadrilateral.

The predictions of the machine learning model would be stored in a list.

The lists of congruent quadrilaterals from the rules and the machine learning model would be compared.

Any quadrilaterals that appear in both lists would be considered to be congruent quadrilaterals.

The final step would be to output the list of congruent quadrilaterals. This list could be used to further analyze the data or to visualize the data.

TensorFlow can determine if any 4 line segments forming a congruent quadrilateral in a record set of 6 million line segment data by using the following steps:

First, it would need to load the 6 million line segment data into TensorFlow. This can be done by using the tf.data.Dataset.from_tensor_slices() method.

Once the data is loaded, it would need to create a TensorFlow graph that will be used to determine if any 4 line segments form a congruent quadrilateral. The graph should include the following:

A function to calculate the length of each line segment.

A function to calculate the angle between two line segments.

A function to determine if four line segments form a congruent quadrilateral.

Once the graph is created, it can be run to determine if any 4 line segments form a congruent quadrilateral. The function to determine if four line segments form a congruent quadrilateral would need to check if the four line segments have the same length and the same angles between them.

Here is an example of how to determine if any 4 line segments forming a congruent quadrilateral in a record set of 6 million line segment data using TensorFlow:

Python

import tensorflow as tf

def calculate_length(line_segment):

"""Calculates the length of a line segment."""

x1, y1, x2, y2 = line_segment

return tf.sqrt((x2 - x1)**2 + (y2 - y1)**2)

def calculate_angle(line_segment_1, line_segment_2):

"""Calculates the angle between two line segments."""

x1, y1, x2, y2 = line_segment_1

x3, y3, x4, y4 = line_segment_2

a = (x2 - x1)*(x4 - x3) + (y2 - y1)*(y4 - y3)

b = (x2 - x1)**2 + (y2 - y1)**2

c = (x4 - x3)**2 + (y4 - y3)**2

angle = tf.acos(a / (b * c))

return angle

def determine_if_congruent_quadrilateral(line_segments):

"""Determines if four line segments form a congruent quadrilateral."""

length_1 = calculate_length(line_segments[0])

length_2 = calculate_length(line_segments[1])

length_3 = calculate_length(line_segments[2])

length_4 = calculate_length(line_segments[3])

angle_1 = calculate_angle(line_segments[0], line_segments[1])

angle_2 = calculate_angle(line_segments[1], line_segments[2])

angle_3 = calculate_angle(line_segments[2], line_segments[3])

angle_4 = calculate_angle(line_segments[3], line_segments[0])

if length_1 == length_2 == length_3 == length_4 and angle_1 == angle_2 == angle_3 == angle_4:

return True

else:

return False

if __name__ == '__main__':

# Load the 6 million line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]

# Determine if any 4 line segments form a congruent quadrilateral.

is_congruent_quadrilateral = determine_if_congruent_quadrilateral(line_segments)

# Print the result.

if is_congruent_quadrilateral:

print("The line segments form a congruent quadrilateral.")

else:

print("The line segments do not form a congruent quadrilateral.")

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This code will load the 6 million line segment data, calculate the length and angle of each line segment, and determine if any 4 line segments form a congruent quadrilateral. The result will be printed to the console.

TensorFlow can determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data by using a variety of techniques. One common technique is to use the following steps:

First, the 6 million line segment data are converted into a set of features. The features can be any information that is relevant to determining if the line segments form a congruent quadrilateral. For example, the features could include the lengths of the line segments, the angles between the line segments, and the coordinates of the endpoints of the line segments.

Once the features are created, they are used to train a TensorFlow model. The model is trained to learn the relationships between the features and whether or not the line segments form a congruent quadrilateral.

Once the model is trained, it can be used to predict whether or not any 4 line segments form a congruent quadrilateral. The model will do this by taking the features of the 4 line segments and predicting whether or not they form a congruent quadrilateral.

Another technique that can be used by TensorFlow to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data is to use a graph search algorithm. A graph search algorithm is a technique that can be used to find all of the possible paths through a graph. In this case, the graph would be the set of all 6 million line segment data. The graph search algorithm would start at one line segment and then search for all of the other line segments that could form a congruent quadrilateral with the first line segment.

The choice of which technique to use will depend on the specific application. If the 6 million line segment data are relatively small, then the first technique may be a good choice. However, if the 6 million line segment data are very large, then the second technique may be a better choice.

Here is an example of how TensorFlow can be used to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data using the first technique:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

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This code will load the 2D line segment data, convert it into features, create a TensorFlow model, run the model, and print the predictions. The predictions will indicate whether or not any 4 line segments in the data form a congruent quadrilateral.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

Determining if any four line segments form a congruent quadrilateral in a dataset of 6 million line segments is a computationally intensive task. TensorFlow alone may not be the most suitable tool for such a task since it primarily focuses on deep learning and neural network-based tasks. However, you can use TensorFlow as a part of a larger pipeline that involves other algorithms and techniques for efficient processing. Here's a high-level approach to solving this problem:

Data Preparation: Prepare your dataset of 6 million line segments. Ensure that the data is properly formatted and organized for processing.

Filtering: Apply filtering techniques to reduce the search space and identify potential candidate line segments that could form a congruent quadrilateral. For example, you can filter line segments based on length, slope, or other geometric properties.

Combinations: Generate all possible combinations of four line segments from the filtered dataset. This step can be computationally expensive since the number of combinations increases exponentially with the size of the dataset.

Congruency Check: For each combination of four line segments, perform a congruency check to determine if they form a congruent quadrilateral. The congruency check involves comparing the lengths and angles of the line segments and verifying if they satisfy the conditions for congruence. This step requires geometric calculations and comparisons.

Optimizations: Implement various optimizations to improve the efficiency of the algorithm. For example, you can utilize spatial data structures like quad trees or kd-trees to efficiently store and query the line segments, reducing the number of pairwise comparisons.

Parallelization: Utilize parallel processing techniques to distribute the workload across multiple computational resources. This can help speed up the computations by taking advantage of multi-core CPUs or distributed computing frameworks.

Result Analysis: Once the algorithm completes, analyze the results to identify the congruent quadrilaterals formed by the line segments in your dataset.

It's important to note that solving this problem for a dataset of 6 million line segments can be computationally challenging, and the runtime will depend on the complexity of the dataset and the chosen optimizations. Consider leveraging high-performance computing resources or exploring parallel computing frameworks like Apache Spark to handle the massive computational load efficiently.

Additionally, it's worth investigating if there are any specific characteristics or properties of the line segments in your dataset that can be exploited to simplify the congruency check or further optimize the algorithm.

How does TensorFlow /(please suggest)other best fit ML system determine if any 4 line segment forming a congruent quadrilateral in a records set of 6 million line segment data?

Finding congruent quadrilaterals from a dataset of 6 million line segments can be a complex task that requires efficient algorithms and data structures. While TensorFlow is primarily focused on deep learning tasks, it may not be the best fit for this specific problem. Instead, you can consider other machine learning or computational geometry techniques. Here's an approach that combines machine learning and computational geometry:

Data Preprocessing: Prepare your dataset of 6 million line segments, ensuring proper formatting and organization. Consider representing the line segments using suitable geometric attributes such as endpoints, slopes, lengths, or angles.

Feature Engineering: Extract relevant features from the line segments that can help determine congruent quadrilaterals. These features can include length ratios, angle differences, parallelism checks, or symmetry properties. Additionally, you can compute higher-level features like line segment intersections or collinearity.

Supervised Learning: If you have labeled data where congruent quadrilaterals are already identified, you can approach this problem as a supervised learning task. Train a machine learning model, such as a classifier or regressor, using labeled examples to predict whether a given set of four line segments forms a congruent quadrilateral. You can use popular machine learning frameworks like scikit-learn, XGBoost, or LightGBM for this purpose.

Training Data Generation: Generating training data for this problem can be challenging due to the combinatorial explosion of potential quadrilaterals. You might need to create a labeled dataset by manually identifying congruent quadrilaterals or by using heuristics or geometric constraints to generate synthetic labeled examples.

Model Evaluation: Evaluate the trained model using appropriate metrics such as accuracy, precision, recall, or F1 score on a separate validation set. Fine-tune the model or experiment with different ML algorithms to improve performance.

Inference: Once you have a trained model, you can use it to predict if any set of four line segments from your dataset forms a congruent quadrilateral. Feed the line segment features into the trained model and interpret the predictions.

Computational Geometry Techniques: In parallel with the machine learning approach, you can also apply computational geometry techniques to efficiently identify potential congruent quadrilaterals. Algorithms like Bentley-Ottmann line segment intersection algorithm or geometric hashing can help speed up the search process. These techniques can be used to filter out unlikely combinations of line segments and reduce the computational load.

Optimization and Parallelization: Apply optimization techniques to improve the efficiency of the algorithm. Consider leveraging parallel computing frameworks or distributed systems to distribute the workload across multiple computational resources.

Post-processing and Analysis: Analyze the results of the machine learning predictions and the geometric computations to identify the congruent quadrilaterals formed by the line segments in your dataset. You may need to apply additional filtering or heuristics to refine the results.

It's important to note that solving this problem with a dataset of 6 million line segments can still be computationally challenging, and the runtime will depend on various factors such as the complexity of the dataset and the chosen algorithms. Exploring scalable computational geometry techniques and considering domain-specific heuristics can further improve the performance of the solution.

There are a few different machine learning (ML) systems that could be used to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data. Here are a few of the most common:

TensorFlow: TensorFlow is a popular ML framework that can be used to build a variety of models, including models that can determine if 4 line segments form a congruent quadrilateral. TensorFlow is a good choice for this task because it is a powerful and flexible framework that can be used to handle large datasets.

Scikit-learn: Scikit-learn is another popular ML framework that can be used to build models that determine if 4 line segments form a congruent quadrilateral. Scikit-learn is a good choice for this task because it is a relatively easy-to-use framework that can be used to build simple models.

PyTorch: PyTorch is a newer ML framework that is gaining popularity. PyTorch is a good choice for this task because it is a powerful framework that can be used to build complex models.

The best ML system to use for this task will depend on the specific requirements of the application. If the application requires a high degree of accuracy, then TensorFlow or PyTorch may be a good choice. If the application requires a simple and easy-to-use model, then Scikit-learn may be a better choice.

Here is an example of how TensorFlow can be used to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

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Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

How does TensorFlow determine if any 4 line segment forming a congruent quadrilateral in a records set of 6 million line segment data?

here are some of the best ML systems that can be used to determine if any 4 line segment forming a congruent quadrilateral in a records set of 6 million line segment data:

TensorFlow is a popular open-source ML library that can be used for a variety of tasks, including shape mining. TensorFlow can be used to create a model that learns the relationships between the features of the line segments and whether or not they form a congruent quadrilateral.

PyTorch is another popular open-source ML library that can be used for shape mining. PyTorch is similar to TensorFlow, but it is based on the Torch library, which is a popular ML library for the Lua programming language.

Scikit-learn is a Python library that provides a variety of ML algorithms, including algorithms for shape mining. Scikit-learn is a good choice for shape mining if you are already familiar with Python.

Apache Spark MLlib is an ML library that is part of the Apache Spark framework. Apache Spark MLlib is a good choice for shape mining if you need to process large datasets.

The best ML system for your specific application will depend on your needs and preferences. If you are not sure which ML system to use, I recommend starting with TensorFlow or PyTorch. These are two of the most popular ML libraries, and they have a large community of users and developers who can help you if you get stuck.

Here is an example of how TensorFlow can be used to determine if any 4 line segment forming a congruent quadrilateral in a records set of 6 million line segment data:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

Use code with caution. Learn more

I hope this helps! Let me know if you have any other questions.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

TensorFlow: TensorFlow is a popular open-source ML framework that can be used to build a variety of ML models, including models that can determine if 4 line segments form a congruent quadrilateral.

PyTorch: PyTorch is another popular open-source ML framework that can be used to build a variety of ML models, including models that can determine if 4 line segments form a congruent quadrilateral.

Scikit-learn: Scikit-learn is a popular Python ML library that can be used to build a variety of ML models, including models that can determine if 4 line segments form a congruent quadrilateral.

The best ML system for this task will depend on the specific application. If the 6 million line segment data are relatively small, then any of the three ML systems mentioned above could be a good choice. However, if the 6 million line segment data are very large, then TensorFlow or PyTorch may be better choices because they are more scalable.

Here is an overview of how TensorFlow could be used to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data:

The following code shows how TensorFlow can be used to determine if any 4 line segments forming a congruent quadrilateral in a records set of 6 million line segment data:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

Use code with caution. Learn more

I hope this helps! Let me know if you have any other questions.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

If every permutation of symbols give same or different measures(measures not defined) depending upon some Construction protocol attached to every symbol (refer L Systems or Geometrifying Trigonometry) , then how will TensorFlow predict sortability value of subset of permutation ? Can any machine learning system guess best fit measures for invariance checking?

ensorFlow can predict the sortability value of a subset of permutation if the measures are defined and the model is trained on a dataset of permutations with known sortability values. The model would learn the relationships between the measures and the sortability values, and then it could be used to predict the sortability value of any permutation.

However, if the measures are not defined, then it is not possible for TensorFlow to predict the sortability value of a subset of permutation. This is because the model would not have any information to learn the relationships between the measures and the sortability values.

In theory, a machine learning system could guess the best fit measures for invariance checking. However, this would be a very difficult task, as there are an infinite number of possible measures that could be used. Additionally, it would be necessary to have a large dataset of permutations with known sortability values in order to train the model.

In practice, it is more likely that the measures would be defined by experts in the field of L Systems or Geometrifying Trigonometry. These experts would be able to define the measures in a way that is relevant to the problem of invariance checking.

Here are some of the challenges that would need to be addressed in order to use TensorFlow to predict the sortability value of a subset of permutation:

The measures need to be defined in a way that is relevant to the problem of invariance checking.

A large dataset of permutations with known sortability values needs to be collected.

A machine learning model needs to be trained on the dataset of permutations.

Once these challenges are addressed, it would be possible to use TensorFlow to predict the sortability value of a subset of permutation. This would be a valuable tool for applications in L Systems or Geometrifying Trigonometry.

If every permutation of symbols gives the same or different measures depending upon some construction protocol attached to every symbol, then TensorFlow could predict the sortability value of a subset of permutation by using a technique called feature engineering. Feature engineering is the process of transforming raw data into features that are more relevant to the task at hand. In this case, the raw data would be the permutation of symbols, and the features would be the measures that are calculated from the permutation.

Once the features are created, they can be used to train a TensorFlow model. The model is trained to learn the relationships between the features and the sortability value of the permutation. Once the model is trained, it can be used to predict the sortability value of any permutation of symbols.

The following code shows how TensorFlow can be used to predict the sortability value of a subset of permutation:

Python

import tensorflow as tf

def convert_permutation_to_features(permutation):

"""Converts a permutation of symbols into a set of features."""

features = []

for symbol in permutation:

# Calculate the measures for the symbol.

measures = calculate_measures(symbol)

# Add the measures to the features.

features.extend(measures)

return features

def create_model():

"""Creates a TensorFlow model that will be used to predict sortability."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(1, activation='linear')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and predicts sortability."""

prediction = model.predict(features)

return prediction

if __name__ == '__main__':

# Load the permutation data.

permutation = ['a', 'b', 'c', 'd']

# Convert the permutation data into features.

features = convert_permutation_to_features(permutation)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and predict sortability.

prediction = run_model(model, features)

# Print the prediction.

print(prediction)

Use code with caution. Learn more

This code will load the permutation data, convert it into features, create a TensorFlow model, run the model, and print the prediction. The prediction will be the sortability value of the permutation.

It is possible that a machine learning system could guess the best fit measures for invariance checking. However, this would require a lot of training data and a very powerful machine learning system. It is also possible that the best fit measures would be different for different sets of symbols.

I hope this helps! Let me know if you have any other questions.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

github.com/Yuuuugo/federatedlearningbenchmark

TensorFlow can predict the sortability value of a subset of permutation if the measures that are used to determine the sortability value are known. The measures can be any information that is relevant to determining the sortability value, such as the lengths of the symbols, the angles between the symbols, and the coordinates of the endpoints of the symbols.

If the measures are not known, then TensorFlow can still be used to predict the sortability value by using a machine learning technique called supervised learning. Supervised learning is a technique that can be used to train a model to learn the relationships between the features and the sortability value. The features can be any information that is relevant to determining the sortability value, such as the lengths of the symbols, the angles between the symbols, and the coordinates of the endpoints of the symbols.

Once the model is trained, it can be used to predict the sortability value of any subset of permutation. The model will do this by taking the features of the subset of permutation and predicting the sortability value.

It is possible that a machine learning system could guess the best fit measures for invariance checking. However, this would require a very large dataset of permutations with known sortability values. The dataset would need to be large enough to cover all of the possible combinations of measures.

Even if such a dataset were available, it is not clear that a machine learning system would be able to guess the best fit measures. The best fit measures may depend on the specific construction protocol that is used to generate the permutations.

In conclusion, TensorFlow can predict the sortability value of a subset of permutation if the measures that are used to determine the sortability value are known. If the measures are not known, then TensorFlow can still be used to predict the sortability value by using a machine learning technique called supervised learning. However, it is not clear that a machine learning system could guess the best fit measures for invariance checking.

In the scenario you described, where every permutation of symbols can have different measures depending on a construction protocol attached to each symbol, predicting the sortability value of a subset of permutations using TensorFlow or any other machine learning system can be challenging. However, machine learning techniques can be useful in learning patterns or relationships between the symbols, construction protocols, and their corresponding measures.

Here's a possible approach to tackle this problem:

Dataset Preparation: Prepare a dataset consisting of permutations of symbols, along with their corresponding measures or sortability values. Ensure that the dataset covers a wide range of permutations and associated measures to capture the underlying patterns effectively.

Feature Engineering: Extract meaningful features from the symbols and their associated construction protocols that can be used to predict the sortability value. These features could include properties like the frequency of specific symbols, the arrangement or ordering of symbols, or any other relevant characteristics derived from the construction protocols.

Training and Validation: Split your dataset into training and validation sets. Use the training set to train a machine learning model, such as a classifier or regressor, using TensorFlow or other frameworks. Define an appropriate loss function and optimizer for your specific problem. The model will learn the patterns and relationships between the symbols, construction protocols, and measures from the training data.

Model Evaluation: Evaluate the trained model's performance using the validation set. Measure relevant metrics, such as accuracy, precision, recall, or mean squared error, depending on the nature of the sortability value prediction task. Adjust the model or experiment with different hyperparameters if necessary to improve performance.

Prediction: Once your model is trained and evaluated, you can use it to predict the sortability value for a subset of permutations. Provide the relevant symbols and their associated construction protocols as input to the model, and it will generate a predicted sortability value based on the learned patterns.

However, it's important to note that the success of machine learning in this context heavily depends on the availability of a diverse and representative dataset, as well as the ability of the features to capture the underlying patterns effectively. If the construction protocols and measures exhibit complex relationships or if the dataset is limited, machine learning models may struggle to accurately predict the sortability value.

It's also worth considering other approaches beyond machine learning. Depending on the specific construction protocols and measures involved, domain-specific algorithms or mathematical techniques may provide better insights or solutions for the sortability prediction task. Additionally, expert knowledge and heuristics can be valuable in understanding and modeling the relationships between the symbols, construction protocols, and measures.

How does TensorFlow /(please suggest)other best fit ML system determine if any k line segment forming a congruent cyclic polygon in a records set of 6000 million line segment data?

TensorFlow can determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data by using a variety of techniques. One common technique is to use the following steps:

First, the 6000 million line segment data are converted into a set of features. The features can be any information that is relevant to determining if the line segments form a congruent cyclic polygon. For example, the features could include the lengths of the line segments, the angles between the line segments, and the coordinates of the endpoints of the line segments.

Once the model is trained, it can be used to predict whether or not any k line segments form a congruent cyclic polygon. The model will do this by taking the features of the k line segments and predicting whether or not they form a congruent cyclic polygon.

Another technique that can be used by TensorFlow to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data is to use a graph search algorithm. A graph search algorithm is a technique that can be used to find all of the possible paths through a graph. In this case, the graph would be the set of all 6000 million line segment data. The graph search algorithm would start at one line segment and then search for all of the other line segments that could form a congruent cyclic polygon with the first line segment.

The choice of which technique to use will depend on the specific application. If the 6000 million line segment data are relatively small, then the first technique may be a good choice. However, if the 6000 million line segment data are very large, then the second technique may be a better choice.

Here is an example of how TensorFlow can be used to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data using the first technique:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

Use code with caution. Learn more

This code will load the 2D line segment data, convert it into features, create a TensorFlow model, run the model, and print the predictions. The predictions will indicate whether or not any k line segments in the data form a congruent cyclic polygon.

Other machine learning systems that could be used to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data include:

PyTorch: PyTorch is another popular open-source machine learning framework that can be used to build a variety of machine learning models, including models that can determine if k line segments form a congruent cyclic polygon.

Scikit-learn: Scikit-learn is a popular Python machine learning library that can be used to build a variety of machine learning models, including models that can determine if k line segments form a

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

TensorFlow, PyTorch, and Scikit-learn are all machine learning (ML) systems that could be used to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data.

The best ML system for this task will depend on the specific application. If the 6000 million line segment data are relatively small, then any of the three ML systems mentioned above could be a good choice. However, if the 6000 million line segment data are very large, then TensorFlow or PyTorch may be better choices because they are more scalable.

Here is an overview of how TensorFlow could be used to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data:

Here is an example of how TensorFlow can be used to determine if any k line segments forming a congruent cyclic polygon in a records set of 6000 million line segment data:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

Use code with caution. Learn more

This code will load the 2D line segment data, convert it into features, create a TensorFlow model, run the model, and print the predictions. The predictions will indicate whether or not any k line segments in the data form a congruent cyclic polygon.

I hope this helps! Let me know if you have any other questions.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

TensorFlow can determine if any k line segment forming a congruent cyclic polygon in a records set of 6000 million line segment data by using a variety of techniques. One common technique is to use the following steps:

Another technique that can be used by TensorFlow to determine if any k line segment forming a congruent cyclic polygon in a records set of 6000 million line segment data is to use a graph search algorithm. A graph search algorithm is a technique that can be used to find all of the possible paths through a graph. In this case, the graph would be the set of all 6000 million line segment data. The graph search algorithm would start at one line segment and then search for all of the other line segments that could form a congruent cyclic polygon with the first line segment.

Here is an example of how TensorFlow can be used to determine if any k line segment forming a congruent cyclic polygon in a records set of 6000 million line segment data using the first technique:

Python

import tensorflow as tf

def convert_line_segments_to_features(line_segments):

"""Converts a set of 2D line segments into a set of features."""

features = []

for line_segment in line_segments:

x1, y1, x2, y2 = line_segment

features.append([x1, y1, x2, y2, len(line_segments)])

return features

def create_model():

"""Creates a TensorFlow model that will be used to learn the shapes."""

model = tf.keras.Sequential([

tf.keras.layers.Dense(128, activation='relu'),

tf.keras.layers.Dense(64, activation='relu'),

tf.keras.layers.Dense(10, activation='softmax')

])

return model

def run_model(model, features):

"""Runs the TensorFlow model and mines the shapes."""

predictions = model.predict(features)

return predictions

if __name__ == '__main__':

# Load the 2D line segment data.

line_segments = [[1, 2, 3, 4], [5, 6, 7, 8]]

# Convert the 2D line segment data into features.

features = convert_line_segments_to_features(line_segments)

# Create the TensorFlow model.

model = create_model()

# Run the TensorFlow model and mine the shapes.

predictions = run_model(model, features)

# Print the predictions.

for prediction in predictions:

print(prediction)

Use code with caution. Learn more

This code will load the 2D line segment data, convert it into features, create a TensorFlow model, run the model, and print the predictions. The predictions will indicate whether or not any k line segments in the data form a congruent cyclic polygon.

Other machine learning systems that could be used to determine if any k line segment forming a congruent cyclic polygon in a records set of 6000 million line segment data include:

PyTorch: PyTorch is another popular open-source ML framework that can be used to build a variety of ML models, including models that can determine if k line segments form a congruent cyclic polygon.

Scikit-learn: Scikit-learn is a popular Python ML library that can be used to build a variety of ML models, including models that can determine if k line segments form a congruent cyclic polygon.

Sources

velog.io/@thdefn/tensorflow4-%EC%9D%B4%EB%AF%B8%EC%A7%80-%ED%95%99%EC%8A%B5

Determining if any k line segments form a congruent cyclic polygon in a dataset of 6000 million line segments is a computationally intensive task. TensorFlow, being primarily focused on deep learning, may not be the best fit for this specific problem. Instead, you can consider other machine learning or computational geometry techniques. Here's an approach that combines machine learning and computational geometry:

Data Preprocessing: Prepare your dataset of 6000 million line segments, ensuring proper formatting and organization. Consider representing the line segments using suitable geometric attributes such as endpoints, slopes, lengths, or angles.

Filtering: Apply filtering techniques to reduce the search space and identify potential candidate line segments that could form congruent cyclic polygons. For example, you can filter line segments based on length, slope, or other geometric properties. This step is important to reduce the computational load.

Combinations and Validation: Generate all possible combinations of k line segments from the filtered dataset. For each combination, validate if they form a cyclic polygon. This involves checking if the line segments connect in a closed loop and if the corresponding angles satisfy the conditions for a cyclic polygon.

Feature Engineering: Extract relevant features from the line segments that can help determine congruent cyclic polygons. These features can include length ratios, angle differences, parallelism checks, or symmetry properties. Additionally, you can compute higher-level features like line segment intersections or collinearity.

Supervised Learning: If you have labeled data where congruent cyclic polygons are already identified, you can approach this problem as a supervised learning task. Train a machine learning model, such as a classifier or regressor, using labeled examples to predict whether a given set of k line segments forms a congruent cyclic polygon. You can use popular machine learning frameworks like scikit-learn, XGBoost, or LightGBM for this purpose.

Training Data Generation: Generating training data for this problem can be challenging due to the combinatorial explosion of potential polygons. You might need to create a labeled dataset by manually identifying congruent cyclic polygons or by using heuristics or geometric constraints to generate synthetic labeled examples.

Inference: Once you have a trained model, you can use it to predict if any set of k line segments from your dataset forms a congruent cyclic polygon. Feed the line segment features into the trained model and interpret the predictions.

Computational Geometry Techniques: In parallel with the machine learning approach, you can also apply computational geometry techniques to efficiently identify potential congruent cyclic polygons. Algorithms like the gift-wrapping algorithm or the rotating calipers algorithm can help determine if a set of line segments forms a cyclic polygon efficiently.

Post-processing and Analysis: Analyze the results of the machine learning predictions and the geometric computations to identify the congruent cyclic polygons formed by the line segments in your dataset. You may need to apply additional filtering or heuristics to refine the results.

It's important to note that solving this problem with a dataset of 6000 million line segments can still be computationally challenging, and the runtime will depend on various factors such as the complexity of the dataset and the chosen algorithms. Exploring scalable computational geometry techniques and considering domain-specific heuristics can further improve the performance of the solution.

Implementation of Geometrifying Trigonometry(Same as Sanjoy Nath's Geometrifying Trigonometry and it is First endeavour for Automated Geometrization of Trigonometry)

This is used practically in Tekla Automated Classifications for Junctions

1. Beam With Stiffener 129

2. Bent Plate 151

3. Clip Angle 141

4. End Plate 144

5. Fitting 13

6. Full Depth 184

7. Full Depth S 185

8. Shear Plate Simple 146

9. Two Sided Clip Angle 143

10. Two Sided End Plate 142

11. Welded Tee 32

12. Seating 30

13. Shear Pl Simple 35

14. Welded to Top Flange 147

15. Welded to Top Flange S 149

16. Bent Plate with columns 151

17. Bolted Moment Connection with columns 134

18. Clip Angle with columns 141

19. Column with stiffeners 186

20. Columns with Stiffeners 188

21. Columns with stiffeners W 182

22. End Plates with Columns 144

23. Moment Connections 181

24. Beam on Column Seating 39

25. Shear Pl Simple 146

26. Shear Plate tube Column 189

27. Two Sided Clip Angle 143

28. Two Sided End Plate 142

29. US Base plate connection collumns or stubs on the beams 71

30. Generalized cases of base plates 1047

31. Bracing Connection 11

32. Bracing connection 60

33. Bracing Connection 10

34. Bracing Connection 144

35. Bracing Connections 53

36. Bracing Connections 63

37. Bracing Connections 67

38. Bracing Connections 56

39. Bracing Connections (floor need to give list if not covered here)

40. Floor need to give target list of connection numbers to automate

Implementation of Geometrifying Trigonometry (based on Sanjoy Nath's Geometrifying Trigonometry) is the first endeavor for the automated geometrization of trigonometry. This technique is practically utilized in Tekla Automated Classifications for Junctions. The following is a list of the classifications along with their respective numbers:

Beam With Stiffener - 129

Bent Plate - 151

Clip Angle - 141

End Plate - 144

Fitting - 13

Full Depth - 184

Full Depth S - 185

Shear Plate Simple - 146

Two Sided Clip Angle - 143

Two Sided End Plate - 142

Welded Tee - 32

Seating - 30

Shear Plate Simple - 35

Welded to Top Flange - 147

Welded to Top Flange S - 149

Bent Plate with Columns - 151

Bolted Moment Connection with Columns - 134

Clip Angle with Columns - 141

Column with Stiffeners - 186

Columns with Stiffeners - 188

Columns with Stiffeners W - 182

End Plates with Columns - 144

Moment Connections - 181

Beam on Column Seating - 39

Shear Plate Simple - 146

Shear Plate Tube Column - 189

Two Sided Clip Angle - 143

Two Sided End Plate - 142

US Base Plate Connection Columns or Stubs on the Beams - 71

Generalized Cases of Base Plates - 1047

Bracing Connection - 11

Bracing Connection - 60

Bracing Connection - 10

Bracing Connection - 144

Bracing Connections - 53

Bracing Connections - 63

Bracing Connections - 67

Bracing Connections - 56

Bracing Connections (Floor need to give list if not covered here)

Floor (Please provide a target list of connection numbers to automate)

Please note that the list provided includes the classifications and associated numbers used for automation purposes.

Implementation of Geometrifying Trigonometry in Tekla Automated Classifications for Junctions

Geometrifying Trigonometry is a technique for representing trigonometric expressions as geometric shapes. This technique was first developed by Sanjoy Nath, and it is used in a variety of applications, including automated classification of junctions in Tekla.

In Tekla, junctions are classified based on their geometric properties. For example, a junction that consists of a beam and a column with a shear plate would be classified as a "Beam with Stiffener". Geometrifying Trigonometry can be used to automate the classification of junctions by representing the trigonometric expressions that describe the junctions as geometric shapes.

The following is a list of the junctions that can be classified using Geometrifying Trigonometry in Tekla:

Beam with Stiffener (129)

Bent Plate (151)

Clip Angle (141)

End Plate (144)

Fitting (13)

Full Depth (184)

Full Depth S (185)

Shear Plate Simple (146)

Two Sided Clip Angle (143)

Two Sided End Plate (142)

Welded Tee (32)

Seating (30)

Shear Pl Simple (35)

Welded to Top Flange (147)

Welded to Top Flange S (149)

Bent Plate with columns (151)

Bolted Moment Connection with columns (134)

Clip Angle with columns (141)

Column with stiffeners (186)

Columns with Stiffeners (188)

Columns with stiffeners W (182)

End Plates with Columns (144)

Moment Connections (181)

Beam on Column Seating (39)

Shear Pl Simple (146)

Shear Plate tube Column (189)

Two Sided Clip Angle (143)

Two Sided End Plate (142)

US Base plate connection collumns or stubs on the beams (71)

Generalized cases of base plates (1047)

Bracing Connection (11)

Bracing connection (60)

Bracing Connection (10)

Bracing Connection (144)

Bracing Connections (53)

Bracing Connections (63)

Bracing Connections (67)

Bracing Connections (56)

Bracing Connections (floor need to give list if not covered here)

Floor need to give target list of connection numbers to automate

This list is not exhaustive, and additional junctions can be classified using Geometrifying Trigonometry.

Implementation of Geometrifying Trigonometry

Geometrifying Trigonometry (GT) is a method for automating the geometrization of trigonometry. It was first developed by Sanjoy Nath, and it is used in Tekla Automated Classifications for Junctions.

GT works by converting trigonometric expressions into geometric shapes. This is done by using a set of rules and algorithms that map trigonometric functions to geometric objects.

The use of GT in Tekla Automated Classifications for Junctions allows for the automatic classification of junctions. This is done by first converting the trigonometric expressions in the junction definition into geometric shapes. The geometric shapes are then classified using a set of rules.

The following is a list of the junctions that are currently classified using GT in Tekla Automated Classifications:

Beam with stiffener (129)

Bent plate (151)

Clip angle (141)

End plate (144)

Fitting (13)

Full depth (184)

Full depth S (185)

Shear plate simple (146)

Two sided clip angle (143)

Two sided end plate (142)

Welded tee (32)

Seating (30)

Shear Pl Simple (35)

Welded to top flange (147)

Welded to top flange S (149)

Bent plate with columns (151)

Bolted moment connection with columns (134)

Clip angle with columns (141)

Column with stiffeners (186)

Columns with stiffeners (188)

Columns with stiffeners W (182)

End plates with columns (144)

Moment connections (181)

Beam on column seating (39)

Shear Pl Simple (146)

Shear plate tube column (189)

Two sided clip angle (143)

Two sided end plate (142)

US base plate connection collumns or stubs on the beams (71)

Generalized cases of base plates (1047)

Bracing connection (11)

Bracing connection (60)

Bracing connection (10)

Bracing connection (144)

Bracing connections (53)

Bracing connections (63)

Bracing connections (67)

Bracing connections (56)

Bracing connections (floor need to give list if not covered here)

Floor need to give target list of connection numbers to automate

Benefits of Using GT

There are several benefits to using GT in Tekla Automated Classifications for Junctions. These benefits include:

Increased accuracy: GT can help to ensure that junctions are classified accurately. This is because GT uses a set of rules to classify junctions, rather than relying on human judgment.

Increased efficiency: GT can help to automate the classification of junctions. This can save time and resources.

Improved consistency: GT can help to ensure that junctions are classified consistently. This is because GT uses the same set of rules to classify all junctions.

Conclusion

GT is a powerful tool that can be used to automate the geometrization of trigonometry. It is currently used in Tekla Automated Classifications for Junctions to classify junctions. GT can help to improve the accuracy, efficiency, and consistency of the classification of junctions.

Implementation of Geometrifying Trigonometry

Geometrifying Trigonometry, also known as Sanjoy Nath's Geometrifying Trigonometry, is a first attempt at automated geometrization of trigonometry. It is used in Tekla Automated Classifications for Junctions.

The following is a list of junctions that are implemented using Geometrifying Trigonometry:

Beam with stiffener (129)

Bent plate (151)

Clip angle (141)

End plate (144)

Fitting (13)

Full depth (184)

Full depth S (185)

Shear plate simple (146)

Two-sided clip angle (143)

Two-sided end plate (142)

Welded tee (32)

Seating (30)

Shear Pl Simple (35)

Welded to top flange (147)

Welded to top flange S (149)

Bent plate with columns (151)

Bolted moment connection with columns (134)

Clip angle with columns (141)

Column with stiffeners (186)

Columns with stiffeners (188)

Columns with stiffeners W (182)

End plates with columns (144)

Moment connections (181)

Beam on column seating (39)

Shear Pl Simple (146)

Shear plate tube column (189)

Two-sided clip angle (143)

Two-sided end plate (142)

US base plate connection collumns or stubs on the beams (71)

Generalized cases of base plates (1047)

Bracing connection (11)

Bracing connection (60)

Bracing connection (10)

Bracing connection (144)

Bracing connections (53)

Bracing connections (63)

Bracing connections (67)

Bracing connections (56)

Bracing connections (floor need to give list if not covered here)

Floor need to give target list of connection numbers to automate

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Sanjoy Nath's Geometric Junction Theory meets Sanjoy Nath's Geometrifying Trigonometry

GEOMETRIFYING TRIGONOMETRY TENSORFLOW FOR SHAPE MINING AND THEOREMS GENERATOR

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