Editing Openai/68f40a7c-717c-8000-8af6-a222789ef1d8 (section)

=== Assistant: Perfect 👍 — here’s your UTF-8–safe, ready-to-run version of the full script. ===
Perfect 👍 — here’s your UTF-8–safe, ready-to-run version of the full script.
It includes the encoding declaration at the top and replaces problematic degree symbols (°) with "deg" for maximum compatibility on Windows.

===== <syntaxhighlight lang="python"># -''- coding: utf-8 -''- =====
"""
GoldenEllipseSpiralCubeSLIDER.py
Interactive 3D visualization showing how a circle appears as a Golden Ellipse
at specific elevation angles (notably near 51.84 deg — the Great Pyramid angle).
Includes buttons and a real-time elevation slider.
"""

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Button, Slider
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

class GoldenEllipseSpiralCube:
    def __init__(self):
        self.fig = plt.figure(figsize=(16, 10))
        self.ax = self.fig.add_subplot(121, projection='3d')
        self.ax_info = self.fig.add_subplot(122)
        self.ax_info.axis('off')

        # Golden ratio and pyramid constants
        self.phi = (1 + np.sqrt(5)) / 2
        self.pyramid_angle = 51.84

        # Cube vertices and faces
        self.vertices = np.array([
            [-1, -1, -1], [1, -1, -1], [1, 1, -1], [-1, 1, -1],
            [-1, -1, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]
        ])
        self.faces = [
            [0, 1, 2, 3], [4, 5, 6, 7],
            [0, 1, 5, 4], [2, 3, 7, 6],
            [0, 3, 7, 4], [1, 2, 6, 5]
        ]
        self.face_colors = [
            [1, 0, 0, 0.05], [0, 1, 0, 0.05],
            [0, 0, 1, 0.05], [1, 1, 0, 0.05],
            [1, 0, 1, 0.05], [0, 1, 1, 0.05]
        ]

        # Geometry elements
        self.spiral_points = self.create_circle_projection_spiral()
        self.circle_projection = self.create_circle_projection()
        self.golden_ellipse_points = self.create_golden_ellipse_projection()

        # Rotation state
        self.elev = 30
        self.azim = 45
        self.dragging = False
        self.prev_mouse = None

        # Create interactive components
        self.create_buttons()
        self.create_slider()
        self.setup_plot()
        self.setup_info_panel()
        self.connect_events()

    def create_circle_projection_spiral(self):
        t = np.linspace(0, 2 * np.pi, 200)
        spiral_points = []
        for angle in t:
            x = np.cos(angle)
            y = np.sin(angle)
            z = -1 + (angle / (2 '' np.pi)) '' 2
            spiral_points.append([x, y, z])
        return np.array(spiral_points)

    def create_circle_projection(self):
        return np.array([[x, y, 1] for x, y, z in self.spiral_points])

    def create_golden_ellipse_projection(self):
        t = np.linspace(0, 2 * np.pi, 100)
        major_axis = 1.0
        minor_axis = major_axis / self.phi
        ellipse_points = [[major_axis '' np.cos(a), minor_axis '' np.sin(a), 1.0] for a in t]
        return np.array(ellipse_points)

    def calculate_perspective_ellipse(self, view_angle):
        t = np.linspace(0, 2 * np.pi, 100)
        theta = np.radians(view_angle)
        minor_axis = np.cos(theta)
        ellipse_points = [[np.cos(a), minor_axis * np.sin(a), 1.0] for a in t]
        return np.array(ellipse_points)

    def create_buttons(self):
        self.ax_reset = plt.axes([0.3, 0.02, 0.12, 0.04])
        self.ax_golden = plt.axes([0.43, 0.02, 0.15, 0.04])
        self.ax_pyramid = plt.axes([0.59, 0.02, 0.15, 0.04])

        self.button_reset = Button(self.ax_reset, 'Default View')
        self.button_golden = Button(self.ax_golden, 'Golden Ratio View')
        self.button_pyramid = Button(self.ax_pyramid, 'Pyramid Angle View')

        self.button_reset.on_clicked(self.reset_view)
        self.button_golden.on_clicked(self.reset_to_golden_view)
        self.button_pyramid.on_clicked(self.reset_to_pyramid_view)

    def create_slider(self):
        """Add a slider to control elevation angle interactively."""
        slider_ax = plt.axes([0.3, 0.08, 0.45, 0.03])
        self.slider_elev = Slider(
            slider_ax, 'Elevation (deg)', 0, 90, valinit=self.elev, valstep=0.5
        )
        self.slider_elev.on_changed(self.update_elevation)

    def update_elevation(self, val):
        """Update the perspective ellipse dynamically as slider moves."""
        self.elev = self.slider_elev.val
        self.ax.view_init(elev=self.elev, azim=self.azim)

        # Remove existing red dashed ellipse (if any)
        for line in self.ax.lines[:]:
            if line.get_linestyle() == '--':
                line.remove()

        # Draw new perspective ellipse
        perspective_ellipse = self.calculate_perspective_ellipse(self.elev)
        self.ax.plot3D(
            perspective_ellipse[:, 0],
            perspective_ellipse[:, 1],
            perspective_ellipse[:, 2],
            color='red', linewidth=2, linestyle='--', alpha=0.8
        )
        self.fig.canvas.draw_idle()

    def setup_plot(self):
        self.ax.clear()
        # Draw cube
        for i, face in enumerate(self.faces):
            vertices = self.vertices[face]
            poly = Poly3DCollection([vertices], alpha=0.03)
            poly.set_facecolor(self.face_colors[i])
            poly.set_edgecolor('gray')
            poly.set_linewidth=0.5
            self.ax.add_collection3d(poly)

        # Spiral, circle, and golden ellipse
        self.ax.plot3D(*self.spiral_points.T, color='black', linewidth=3, alpha=0.8)
        self.ax.plot3D(*self.circle_projection.T, color='blue', linewidth=3, alpha=0.8)
        self.ax.plot3D(*self.golden_ellipse_points.T, color='gold', linewidth=4, alpha=0.9)

        # Perspective ellipse (initial red dashed)
        perspective_ellipse = self.calculate_perspective_ellipse(self.elev)
        self.ax.plot3D(*perspective_ellipse.T, color='red', linewidth=2, linestyle='--', alpha=0.8)

        # Major/minor axis
        self.ax.plot3D([-1, 1], [0, 0], [1, 1], color='green', linewidth=2)
        minor_axis_length = 1 / self.phi
        self.ax.plot3D([0, 0], [-minor_axis_length, minor_axis_length], [1, 1], color='purple', linewidth=2)

        # Labels
        self.ax.text(0.6, 0, 1.1, '1.000', color='green', fontweight='bold')
        self.ax.text(0.1, minor_axis_length/2, 1.1, f'{minor_axis_length:.3f}', color='purple', fontweight='bold')

        # Limits and style
        self.ax.set_xlim([-1.5, 1.5])
        self.ax.set_ylim([-1.5, 1.5])
        self.ax.set_zlim([-1.5, 1.5])
        self.ax.set_xlabel('X Axis', fontweight='bold')
        self.ax.set_ylabel('Y Axis', fontweight='bold')
        self.ax.set_zlabel('Z Axis', fontweight='bold')
        self.ax.set_title('Golden Ellipse Phenomenon', fontsize=14, fontweight='bold')
        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.fig.canvas.draw_idle()

    def setup_info_panel(self):
        self.ax_info.clear()
        self.ax_info.axis('off')
        minor_axis_length = 1 / self.phi
        pyramid_minor_axis = np.cos(np.radians(self.pyramid_angle))
        pyramid_ratio = 1.0 / pyramid_minor_axis

        legend_text = (
            "VISUAL ELEMENTS EXPLANATION:\n\n"
            "Black: 3D Spiral\n"
            "Blue: Perfect Circle (front)\n"
            "Gold: Golden Ellipse (phi=1.618)\n"
            "Red dashed: Current Perspective\n"
            "Green: Major Axis = 1.000\n"
            "Purple: Minor Axis = 0.618\n\n"
            "GOLDEN RATIO & PYRAMID CONNECTION:\n\n"
            f"phi = {self.phi:.6f}\n"
            f"Pyramid Angle = {self.pyramid_angle} deg\n"
            f"Ratio ≈ {pyramid_ratio:.6f}\n\n"
            "At 51.84 deg: Minor Axis ≈ cos(51.84 deg)\n"
            "→ Matches Golden Ratio visually!\n\n"
            "CONTROLS:\n"
            "- Drag to rotate\n"
            "- Scroll to zoom\n"
            "- Use buttons for presets\n"
            "- Move slider to adjust elevation"
        )
        self.ax_info.text(0.05, 0.95, legend_text, transform=self.ax_info.transAxes,
                         fontsize=9, verticalalignment='top', fontfamily='monospace',
                         bbox=dict(boxstyle="round,pad=1", facecolor='lightblue', alpha=0.8))
        self.fig.canvas.draw_idle()

    def connect_events(self):
        self.fig.canvas.mpl_connect('button_press_event', self.on_press)
        self.fig.canvas.mpl_connect('button_release_event', self.on_release)
        self.fig.canvas.mpl_connect('motion_notify_event', self.on_motion)
        self.fig.canvas.mpl_connect('scroll_event', self.on_scroll)

    def on_press(self, event):
        if event.inaxes == self.ax:
            self.dragging = True
            self.prev_mouse = (event.x, event.y)

    def on_release(self, event):
        self.dragging = False
        self.prev_mouse = None

    def on_motion(self, event):
        if not self.dragging or event.inaxes != self.ax or self.prev_mouse is None:
            return
        dx = event.x - self.prev_mouse[0]
        dy = event.y - self.prev_mouse[1]
        self.azim += dx * 0.5
        self.elev -= dy * 0.5
        self.elev = np.clip(self.elev, 0, 90)
        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.slider_elev.set_val(self.elev)
        self.prev_mouse = (event.x, event.y)
        self.fig.canvas.draw_idle()

    def on_scroll(self, event):
        if event.inaxes == self.ax:
            xlim, ylim, zlim = self.ax.get_xlim(), self.ax.get_ylim(), self.ax.get_zlim()
            xc, yc, zc = np.mean(xlim), np.mean(ylim), np.mean(zlim)
            zoom = 0.9 if event.step > 0 else 1.1
            xr, yr, zr = (xlim[1]-xlim[0])''zoom, (ylim[1]-ylim[0])''zoom, (zlim[1]-zlim[0])*zoom
            self.ax.set_xlim([xc-xr/2, xc+xr/2])
            self.ax.set_ylim([yc-yr/2, yc+yr/2])
            self.ax.set_zlim([zc-zr/2, zc+zr/2])
            self.fig.canvas.draw_idle()

    def reset_view(self, event=None):
        self.elev, self.azim = 30, 45
        self.slider_elev.set_val(self.elev)
        self.setup_plot()

    def reset_to_golden_view(self, event=None):
        self.elev, self.azim = 52, 45
        self.slider_elev.set_val(self.elev)
        self.setup_plot()

    def reset_to_pyramid_view(self, event=None):
        self.elev, self.azim = self.pyramid_angle, 45
        self.slider_elev.set_val(self.elev)
        self.setup_plot()

    def show(self):
        print("GOLDEN ELLIPSE & GREAT PYRAMID CONNECTION")
        print("=" * 50)
        print("At ~51.84 deg elevation → circle appears as golden ellipse (phi≈1.618)")
        plt.show()

=== Run the visualization ===
if __name__ == "__main__":
    cube = GoldenEllipseSpiralCube()
    cube.show()

</syntaxhighlight>

===== Save the file as =====
GoldenEllipseSpiralCubeSLIDER.py

Then in PowerShell or Command Prompt:

<syntaxhighlight lang="bash">py GoldenEllipseSpiralCubeSLIDER.py

</syntaxhighlight>

Would you like me to add a smooth automatic animation that moves the slider back and forth between 0° and 60° (to visually show the ellipse transformation)?