Keçeci Binomial Squares (Keçeci Binom Kareleri): Keçeci's Arithmetical Square (Keçeci Aritmetik Karesi, Keçeci'nin Aritmetik Karesi)

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DOI
License: MIT

Description / Açıklama

Keçeci Binomial Squares (Keçeci Binom Kareleri): Keçeci's Arithmetical Square (Keçeci Aritmetik Karesi, Keçeci'nin Aritmetik Karesi):

Keçeci Binomial Squares (Keçeci Binom Kareleri): The Keçeci Binomial Square is a series of binomial coefficients forming a square region within Khayyam (مثلث خیام), Pascal, Binomial Triangle, selected from a specified starting row with defined size and alignment.

Keçeci Binom Karesi, Hayyam (مثلث خیام), Pascal, Binomial üçgeni içinde belirli bir başlangıç satırından itibaren, seçili boyut ve hizalamada bir kare oluşturan binom katsayıları serisidir.

Installation / Kurulum

```bash conda install bilgi::kececisquares -y

pip install kececisquares ``` https://anaconda.org/bilgi/kececisquares

https://pypi.org/project/kececisquares/

https://github.com/WhiteSymmetry/kececisquares

https://zenodo.org/records/15411671

https://zenodo.org/records/

Usage / Kullanım

Example

```python import matplotlib.pyplot as plt import kececisquares as ks import math # For math.ceil

Cell 2: Function to get user input (optional, you can hardcode for simplicity)

def getuserparameters(): """Gets parameters from the user.""" print("--- Configure Binomial Triangle Visualization ---") try: numrows = int(input("Enter number of rows for Pascal's/Binomial Triangle (e.g., 7, min: 1): ")) if numrows < 1: print("Error: Number of rows must be at least 1.") return None

    practical_max_square_size = math.ceil(num_rows / 2) if num_rows > 1 else 1
    square_size_prompt = (f"Enter square size (1-{num_rows}, e.g., 3, "
                          f"practical max for centered: {practical_max_square_size}): ")
    square_size = int(input(square_size_prompt))
    if not (1 <= square_size <= num_rows):
        print(f"Error: Square size must be between 1 and {num_rows}.")
        return None

    min_start_row_0idx = max(0, square_size - 1)
    max_start_row_0idx = num_rows - square_size
    if min_start_row_0idx > max_start_row_0idx:
        print(f"A {square_size}x{square_size} square cannot be formed in a triangle of {num_rows} rows.")
        return None

    start_row_prompt = (f"Enter starting row for the square "
                        f"(1-indexed, between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}, "
                        f"e.g., {min_start_row_0idx + 1}): ")
    start_row_user = int(input(start_row_prompt))
    start_row_0idx = start_row_user - 1
    if not (min_start_row_0idx <= start_row_0idx <= max_start_row_0idx):
        print(f"Error: Starting row (1-indexed) must be between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}.")
        return None

    shape_prompt = "Shape type (1: hexagon, 2: square, 3: circle, 4: triangle; default: 1-hexagon): "
    shape_choice = input(shape_prompt).strip()
    shape_map = {"1": "hexagon", "2": "square", "3": "circle", "4": "triangle"}
    shape_type = "hexagon"
    if shape_choice == "": print("Defaulting to 'hexagon' (1).")
    elif shape_choice in shape_map: shape_type = shape_map[shape_choice]
    else: print(f"Invalid shape type. Defaulting to 'hexagon' (1).")

    align_prompt = "Square alignment (1: Left, 2: Right, 3: Centered; default: 1-Left): "
    align_choice = input(align_prompt).strip()
    align_map = {"1": "left", "2": "right", "3": "center"}
    alignment = "left"
    if align_choice == "": print("Defaulting to 'Left-Aligned' (1).")
    elif align_choice in align_map: alignment = align_map[align_choice]
    else: print(f"Invalid alignment. Defaulting to 'Left-Aligned' (1).")

    fill_prompt = "Fill the square? (1: Yes, 2: No; default: 1-Yes): "
    fill_choice = input(fill_prompt).strip()
    is_filled = True
    if fill_choice == "1": pass
    elif fill_choice == "2": is_filled = False
    elif fill_choice == "": print("Defaulting to 'Yes' (1).")
    else: print(f"Invalid fill choice. Defaulting to 'Yes' (1).")

    show_val_prompt = "Show numbers inside shapes? (1: Yes, 2: No; default: 1-Yes): "
    show_val_choice = input(show_val_prompt).strip()
    show_numbers = True # Varsayılan
    if show_val_choice == "1": pass
    elif show_val_choice == "2": show_numbers = False
    elif show_val_choice == "": print("Defaulting to show numbers (1).")
    else: print(f"Invalid choice for showing numbers. Defaulting to show numbers (1).")

    return {
        "num_rows": num_rows,
        "square_size": square_size,
        "start_row_0idx": start_row_0idx,
        "shape_type": shape_type,
        "alignment": alignment,
        "is_filled": is_filled,
        "show_numbers": show_numbers, # Yeni parametreyi sözlüğe ekle
    }
except ValueError:
    print("Error: Invalid numerical input.")
    return None
except Exception as e:
    print(f"An unexpected error occurred during input: {e}")
    return None

Cell 3: Get parameters and run the visualization

params = getuserparameters()

if params: print("\n--- Generating Plot ---") # Call the drawing function from the module # Pass showplot=False if you want to manage plt.show() or save the figure later # We let the module handle plt.show() by default for simplicity here. fig, ax = ks.drawkececibinomialsquare( numrowstodraw=params["numrows"], squareregionsize=params["squaresize"], startrowindexforsquare0based=params["startrow0idx"], shapetodraw=params["shapetype"], squarealignment=params["alignment"], issquarefilled=params["isfilled"], showplot=True, # Let the function call plt.show() showvalues=params.get("shownumbers", True) # Yeni parametre, varsayılan True )

if fig:
    print("Plot generated successfully.")
    # You can do more with fig and ax here if needed, e.g., fig.savefig("triangle.png")
else:
    print("Plot generation failed.")

else: print("Could not proceed due to invalid parameters.")

```

License / Lisans

This project is licensed under the MIT License. See the LICENSE file for details.

Citation

If this library was useful to you in your research, please cite us. Following the GitHub citation standards, here is the recommended citation.

BibTeX

```bibtex @misc{kececi202515411670, author = {Keçeci, Mehmet}, title = {kececisquares}, month = may, year = 2025, publisher = {GitHub, PyPI, Anaconda, Zenodo}, version = {0.1.0}, doi = {10.5281/zenodo.15411670}, url = {https://doi.org/10.5281/zenodo.15411670}, }

@misc{kececi202515425855, author = {Keçeci, Mehmet}, title = {The Keçeci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications }, month = may, year = 2025, publisher = {Zenodo}, doi = {10.5281/zenodo.15425855}, url = {https://doi.org/10.5281/zenodo.15425855}, } ```

APA

``` Keçeci, M. (2025). kececisquares [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.15.1

Keçeci, M. (2025). Keçeci's Arithmetical Square. Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1

Keçeci, M. (2025). kececisquares. Zenodo. https://doi.org/10.5281/zenodo.15411670

Keçeci, M. (2025). The Keçeci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications. https://doi.org/10.5281/zenodo.15425855

```

Chicago

``` Keçeci, Mehmet. kececisquares [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.15.1

Keçeci, Mehmet. "Keçeci's Arithmetical Square". Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1

Keçeci, Mehmet. "kececisquares". Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15411670

Keçeci, Mehmet. "The Keçeci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications", 15 Mayıs 2025. https://doi.org/10.5281/zenodo.15425855

```