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1. The First Lines
Geometry is learned by making marks, not by formulas.
2. The Compass
A fixed radius creates repeatable circles and consistent distance.
3. The Straightedge
Points are connected and extended to form structure.
4. Circle and Line
Intersections create the first meaningful geometry.
5. Vesica Piscis
Two circles create symmetry and proportional relationships.
6. Seed of Life
Repeating the vesica builds structured patterns from simple rules.
7. Triangle (from Vesica)
The equilateral triangle emerges as the first stable polygon.
8. Square (Square Demo)
Right angles establish orthogonal structure and layout.
9. The Cubit (Drafting Ratios)
Length is transferred and scaled using a physical unit.
10. Division of a Line
Lengths are split into equal and proportional parts.
11. Ratios
Relationships between lengths matter more than absolute values.
12. √2 (Square Diagonal)
The diagonal introduces the first non-rational relationship.
13. √3 (Triangle Height)
Triangle geometry produces a second fundamental ratio.
14. √5 (Bridge Ratio)
A constructed diagonal enables more complex proportions.
15. Golden Ratio (φ)
A line can divide into a self-repeating proportion.
16. Pi (π)
The circle defines a constant relationship between diameter and circumference.
17. 2π (Full Cycle)
A complete rotation links geometry to cycles and time.
18. Angle from Circle
Rotation is measured as arc, not just length.
19. Constructed Angles (60°, 90°, 120°)
Angles emerge from geometry, not assumption.
20. Build to Euclid 47
Squares constructed on triangle sides reveal area relationships.
21. Euclid’s 47th Proposition
The square on the hypotenuse equals the sum of the other two.
a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
22. Proportion in Shapes
Forms scale consistently through ratio.
23. Layout and Alignment
Grids and reference lines organize space.
24. Geometry in Construction
Structure, stability, and design emerge from proportion.
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