• Saving the ruins ;
• • Introduction ;
• • Revolving crane ;
• • Pile-driver  ;
• • Jacques Demichelis : Goodbye ;
• • Form ;
• • Castles owners ;
• • Castles location ;
• • Public opening time ;
• • Le silence a régné dans la cour du château en 2020 en raison des contraintes sanitaires.
Espérons que la fête de Mézerville aura lieu en 2021 et que l’Association NAMUKA pourra nous proposer un spectacle !

# Squaring the circle

The purpose is to draw a square whose surface is equal to a circle.
If one chooses a circle whose ray is the unit, it is necessary to trace a square whose side is equal to since the surface of the circle is equal to . ## First Part : Geometrical construction of the number (Kochansky method)

• create a circle centered at B, of radius BC = 1 (unit), trace the two diameters AC and OJ, OJ is perpendicular to OJ at A.

• On the AC perpendicular, at C, trace three equals segments

CD = DE = EF = 1 (unit)

• Trace an arc of circle centered at J, of radius JB = 1 (unit), this intersect the main circle at G and K, GK being one of the inscribed equilateral triangle sides

an angle (A B G) = 30°

• Draw BG that intersect the perpendicular in A at H.

The segment FH is equal to ### Demonstration :

• Draw IH, perpendicular at CF

• ABH triangle : tg 30° = AH/AB= 0,57735 (AB = 1 unit)

• HIF right-angled triangle triangle HIF, HI = AC = 2 units

• IF = CF – CI and CI = AH =  0.57735

• HI² +IF² = HF² (IF = 3 – 0.57735)

• HF² = 4 + (3 – 0.57735)²

• So : HF = 9,86923

• HF = 3,141533

## Second part : geometrical construction of • Either FH = , one prolongs FH in M such as HM = 1 (unit) • Let Q be the medium of MF

• Draw the arc of circle MLF (centered on Q)

• Draw HF, perpendicular in H, it intersect the arc of circle at L,

LH = ### Demonstration :

Triangles MFL and LHM are right-angled and similar : LH/HM = FH/LH

Consequently  :

• LH² = HM *FH, HM = 1 (unit)

• LH²= FH = • LH  = ### Conclusion :

The surface of the square LPNH whose side is equal to is close to surface equal to of the circle centered on H and of radius HM = 1.

Back to index

Top of the page
Château de Mézerville ©2020 - Realisation Artisan du Virtuel - V1.7.1-2006-03-14 Page MAJ 12.28.2006