cf. [url=https://www.geogebra.org/m/D6Q9FVXs]GeoGebra's sense is odd.[/url][br]---- GeoGebra's specification of circle intersection is odd.[br][b][br]■ Kempe's reversor[/b][br][url=https://www.geogebra.org/m/Atz6vgBM]Line Symmetry Linkage (Alias: Imai's Butterfly)[/url][br]--- by 5 bars.[br]exact straight line linkage --- by 7 bars.　[br]( Peaucellier exact straight line linkage --- by 7 bars. )[br][b][br]■ Hart's inversor (= Antiparallelogram)[br][/b]--- by 4 bars.[br]exact straight line linkage --- by 5 bars.[br][b][br]Tip: [/b]Peaucellier's inversor is horizontal-symmetric (6 bars), Hart's inversor is vertical-symmetric (4 bars).[br]Element is the same triangle parts. [br]( Hart is a pure mathematician in UK. [br] Peaucellier is not a pure mathematician in France. He was a French army officer. )[b][br][br]■ Hart's A-frame exact line straight linkage[/b][br]--- by 5 bars.[br]cf. [url=https://www.geogebra.org/m/cNnq9YuN]Generalized Hart's A-frame[br][br][/url][b]■ [url=https://en.wikipedia.org/wiki/Spiral]Spiral[/url][/b][br]In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.[br][br][b]■ Conservation law　(like as "conservation law of energy")[/b][br] ●C[br] a |h b[br] |[br]A● + + ●B[br] M H[br][br], where AH = a', HB = b', AM = 0.5(a'+ b') = 0.5 AB, CH = h (= vertical height)[br]then, a[sup]2[/sup] - b[sup]2[/sup] = (a'[sup]2[/sup] + h[sup]2[/sup]) - (b'[sup]2[/sup] + h[sup]2[/sup]) = a'[sup]2[/sup] - b'[sup]2[/sup][br]= (a'+ b')(a'- b') = constant (∵ a, b is constant).[br] also, [br]a'- b' = 2[a'- 0.5(a'+b')] = 2 MH ∽ MH[br]a'+ b' = AB[br]i.e. [b]MH × AB[/b] = constant. ( i.e. if AB increases by N multiple, MH increases by 1/N multiple. ) [br] [br][br]This law is always true for any angle ∠ACB.[br]Conservation law in the triangle geometry. [br][br][b]■ Conservation law of Parallelogram[/b][br]　 C●---------●D[br] / /[br]A●---------●B[br]if, AB = a, AC = b, AB // CD, AC // BD,[br]Then,[br]Q: What is AD[sup]2[/sup] + CB[sup]2[/sup] ?[br]A: [b]2 (a[sup]2[/sup] + b[sup]2[/sup]) [/b]= constant.