Mathematics : Geometric constructions

Theorem of Viviani (Geometric construction of visual proof of FormuLe)

Viviani's theorem, Step-by-step construction of Visual Proof of FormuL^e

[Gallery, Math animations-Geometry, Viviani's theorem (FormuLe's Visual Proof)  -  (locale-Formule)]

: S T E P S   O F   C O S T R U C T I O N :

1. Draw the circle with center at the point P and radius h₂;

2. Draw the intersection point D of the circle 1. and the line through the points H₁, P;

3. Draw the arc DPH₂ and the segment PD (PD = h₂);

4. Draw the line parallel to the side AB passing through the point D;

5. Draw the intersection point between the line 4. and the segment h;

6. Draw the line perpendicular to the side AB passing through the point H₃;

7. Draw the line through the point D parallel to the line through the points P, H₃ ;

8. Draw the intersection point E between the lines 6. e 7.;

9. Draw a circle with center at the point D and radius h₃;

10. Draw the intersection point F of the circle 9. and the line through the points H₁ e P;

11. Draw the arc DEF and the segment DF (DF = h₃);

12. HC = H₁F = H₁P + PD + DF (h = h₁ + h₂ + h₃).

: G I F : CONSTRUCTION : Viviani's Theorem (Visual Demonstration of FormuL^e)