essai

Dérouler le cercle

Périmètre du cercle

Longueur

 ... 

Longueur

a = 360 (slider from 0 to 360, step 1)
diamètre = 3.2 (slider from 0.1 to 4, step 0.1)
I: (((a * 3.141592653589793) * diamètre / 360), diamètre / 2)
K: (x(I), 0)
D = (0, 0)
c = Circle(I, K)
M = Rotate(K, 360° - a°, I)
e = CircleArc(I, K, M)
b = Segment(D, K)
DK = Distance(D, K)
TexteDK: Name[D] + (Name[K]) + " \, = \, " + DK
texte2: DK + ""
cercle = true
longueur = true
A = Center(c)
c_0 = Circle(A, D)
A1_1 = Name(diamètre)
A1_2 = Name(diamètre)
A1_3 = Name(diamètre)
A1_4 = Name(diamètre)
A1_5 = Name(diamètre)
A1 = Name(diamètre)
A3 = 2.9
A4 = 3
A5 = 3.1
A6 = 3.2

Tool: triangle équilatéral (se) (command triangleéquilatéralse)
triangleéquilatéralse[ <Point>, <Point> ]
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Rotate(B, 60*°, A)
b = Segment(C, A)
c = Segment(C, B)

Tool: triangle isocèle (se) (command triangleisocèlese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Point(Circle[A, a])
b = Segment(A, C)
c = Segment(B, C)

Tool: triangle rectangle (se) (command trianglerectanglese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Point(OrthogonalLine[B, Line[A, B]])
b = Segment(B, C)
c = Segment(C, A)

Tool: triangle rectangle isocèle (se) (command trianglerectangleisocèlese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Rotate(B, 90*°, A)
b = Segment(C, A)
c = Segment(C, B)

Tool: carré (se) (command carrése)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Rotate(A, 270*°, B)
D = Rotate(B, 90*°, A)
b = Segment(B, C)
c = Segment(C, D)
d = Segment(D, A)

Tool: rectangle (se) (command rectanglese)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Point(OrthogonalLine[A, Line[A, B]])
b = Segment(C, A)
D = Intersect(OrthogonalLine[C, Line[A, C]], OrthogonalLine[B, Line[A, B]])
c = Segment(C, D)
d = Segment(D, B)

Tool: parallélogramme (se) (command parallélogrammese)
Input: A, B, C
Output: D, a, b, c, d

a = Segment(A, B)
b = Segment(B, C)
D = Point(A, Vector[B, C])
c = Segment(A, D)
d = Segment(D, C)

Tool: losange (se) (command losangese)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Point(Circle[B, a])
b = Segment(B, C)
D = Point(A, Vector[B, C])
c = Segment(A, D)
d = Segment(D, C)

Tool: pavage triangle (command pavagetriangle)
Input: A, B
Output: poly1, C, a, b, c

poly1, a, b, c, C = Polygon(A, B, 3)

Tool: pavage carré (command pavagecarré)
Input: D, E
Output: poly2, F, G, d, e, f, g

poly2, d, e, f, g, F, G = Polygon(D, E, 4)

Tool: pavage pentagone (command pavagepentagone)
Input: H, I
Output: poly3, J, K, L, h, i, j, k, l

poly3, h, i, j, k, l, J, K, L = Polygon(H, I, 5)

Tool: pavage héxagone (command pavagehéxagone)
Input: M, N
Output: poly4, O, P, Q, R, m, n, o, p, q, r

poly4, m, n, o, p, q, r, O, P, Q, R = Polygon(M, N, 6)

Tool: pavage héptagone (command pavagehéptagone)
Input: S, T
Output: poly5, U, V, W, Z, A1, s, t, u, v, w, z, a1

poly5, s, t, u, v, w, z, a1, U, V, W, Z, A1 = Polygon(S, T, 7)

Tool: pavage octogone (command pavageoctogone)
Input: B1, C1
Output: poly6, D1, E1, F1, G1, H1, I1, b1, c1, d1, e1, f1, g1, h1, i1

poly6, b1, c1, d1, e1, f1, g1, h1, i1, D1, E1, F1, G1, H1, I1 = Polygon(B1, C1, 8)

Tool: pavage nonagone (command pavagenonagone)
Input: J1, K1
Output: poly7, L1, M1, N1, O1, P1, Q1, R1, j1, k1, l1, m1, n1, o1, p1, q1, r1

poly7, j1, k1, l1, m1, n1, o1, p1, q1, r1, L1, M1, N1, O1, P1, Q1, R1 = Polygon(J1, K1, 9)

Tool: pavage décagone (command pavagedécagone)
Input: S1, T1
Output: poly8, U1, V1, W1, Z1, A2, B2, C2, D2, s1, t1, u1, v1, w1, z1, a2, b2, c2, d2

poly8, s1, t1, u1, v1, w1, z1, a2, b2, c2, d2, U1, V1, W1, Z1, A2, B2, C2, D2 = Polygon(S1, T1, 10)

Tool: pavage endécagone (command pavageendécagone)
Input: E2, F2
Output: poly9, G2, H2, I2, J2, K2, L2, M2, N2, O2, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2, o2

poly9, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2, o2, G2, H2, I2, J2, K2, L2, M2, N2, O2 = Polygon(E2, F2, 11)

Tool: pavage héxagone (command pavagehéxagon)
Input: M, N
Output: poly4, O, P, Q, R, m, n, o, p, q, r

poly4, m, n, o, p, q, r, O, P, Q, R = Polygon(M, N, 6)

Tool: Guide âne (command Guideâne)
Input: A, B, C
Output: a, D, E, F, G, H, I, J, K, L, M, N, b, c, d, e, f, g, h, i, j, k, l, m

a = Line(A, B)
b = Line(C, a)
D = Translate(C, Vector[B, C])
c = Line(D, b)
E = Translate(D, Vector[B, C])
d = Line(E, c)
F = Translate(E, Vector[B, C])
G = Translate(F, Vector[B, C])
H = Translate(G, Vector[B, C])
e = Line(F, d)
f = Line(G, e)
g = Line(H, f)
I = Translate(H, Vector[B, C])
J = Translate(I, Vector[B, C])
K = Translate(J, Vector[B, C])
h = Line(I, g)
i = Line(J, h)
j = Line(K, i)
L = Translate(K, Vector[B, C])
M = Translate(L, Vector[B, C])
N = Translate(M, Vector[B, C])
k = Line(L, j)
l = Line(M, j)
m = Line(N, l)

Tool: pavage dodécagone (command pavagedodécagone)
Input: P2, Q2
Output: poly10, R2, S2, T2, U2, V2, W2, Z2, A3, B3, C3, p2, q2, r2, s2, t2, u2, v2, w2, z2, a3, b3, c3

poly10, p2, q2, r2, s2, t2, u2, v2, w2, z2, a3, b3, c3, R2, S2, T2, U2, V2, W2, Z2, A3, B3, C3 = Polygon(P2, Q2, 12)

Tool: AnglePresqueDroit
point, sommet, point, précision,taille
Input: A, B, C, prec, r
Output: poly1, a_1, b_1, c_1, d_1, e, e_1, f, g, h, i, j, l, m, n, p, q, s, t

Z = Dilate(A, r / Distance[A, B], B)
b = AngularBisector(A, B, C)
c = Segment(A, C)
D = Intersect(b, c)
A' = Dilate(D, r / ((Distance[D, B] * sqrt(2))), B)
a = Angle(A, B, C)
A'_1 = Dilate(A, Distance[B, C] / Distance[A, B], B)
I = Rotate(A'_1, a, B)
test2 = If(I ≟ C, 1, -1)
test: abs(90° - a) ≤ prec°
F = If(test ≟ true, A', B)
k = If(test ≟ true, 90, (test2 * a / (16°)))
Z' = Rotate(Z, k°, F)
Z'' = Rotate(Z', k°, F)
Z''' = Rotate(Z'', k°, F)
E = Rotate(Z''', k°, F)
E' = Rotate(E, k°, F)
E'' = Rotate(E', k°, F)
E''' = Rotate(E'', k°, F)
G = Rotate(E''', k°, F)
G' = Rotate(G, k°, F)
G'' = Rotate(G', k°, F)
G''' = Rotate(G'', k°, F)
H = Rotate(G''', k°, F)
H' = Rotate(H, k°, F)
H'' = Rotate(H', k°, F)
H''' = Rotate(H'', k°, F)
J = Rotate(H''', k°, F)
poly1, e, f, g, h, i, j, l, m, n, p, q, s, t, a_1, b_1, c_1, d_1, e_1 = Polygon(B, Z, Z', Z'', Z''', E, E', E'', E''', G, G', G'', G''', H, H', H'', H''', J)

Tool: Orthocentre
Sélectionner 3 points
Input: A, B, C
Output: D

poly1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(B, b)
e = OrthogonalLine(A, a)
D = Intersect(d, e)

Tool: Cercle circonscrit (command Cerclecirconscrit)
Sélectionner 3 points
Input: A, B, C
Output: f

poly1, c, a, b = Polygon(A, B, C)
d = LineBisector(c)
e = LineBisector(b)
D = Intersect(d, e)
f = Circle(D, B)

Tool: Cercle inscrit (command Cinscrit)
Sélectionner 3 points
Input: A, B, C
Output: k

poly1, c, a, b = Polygon(A, B, C)
f = AngularBisector(C, A, B)
h = AngularBisector(A, B, C)
D = Intersect(f, h)
i = OrthogonalLine(D, c)
I = Intersect(c, i)
k = Circle(D, I)

Tool: Centre de gravité (command CentreGravité)
Sélectionner 3 points
Input: A, B, C
Output: L

J = Midpoint(B, C)
K = Midpoint(A, C)
p = Segment(A, J)
q = Segment(B, K)
L = Intersect(p, q)

Tool: Cercle (diamètre) (command Outil27)
point, point(extémités du diamètre)
Input: A, B
Output: c

C = Midpoint(A, B)
c = Circle(C, B)