Grid Multiplication

Drag the point inside the rectangle

To work in Integers first select "View-->Grid" then select "Options-->Fixed to Grid"

Method 1:

Method 2:

Ans

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Ans

A = (0, 0)
b = 50 (slider from 0 to 50, step 1)
Bx: (b, 0)
a = 50 (slider from 0 to 50, step 1)
ABxy: (b, a)
Ay: (0, a)
poly5, ay_1, abxy_1, bx_1, a_2 = Polygon(Ay, ABxy, Bx, A)
c = Segment(Ay, ABxy)
d = Segment(ABxy, Bx)
e = Segment(Bx, A)
f = Segment(Ay, A)
B = PointIn(poly5)
g = OrthogonalLine(B, xAxis)
h = OrthogonalLine(B, yAxis)
C = Intersect(g, c)
F = Intersect(h, d)
D = Intersect(h, f)
E = Intersect(g, e)
i = Segment(D, B)
j = Segment(B, F)
k = Segment(C, B)
l = Segment(B, E)
poly1, ay, c_1, b_1, d_1 = Polygon(Ay, C, B, D)
poly2, c_2, abxy, f_1, b_2 = Polygon(C, ABxy, F, B)
poly3, b_3, f_2, bx, e_1 = Polygon(B, F, Bx, E)
poly4, d_2, b_4, e_2, a_1 = Polygon(D, B, E, A)
G = Intersect(i, k)
dAyC = Distance(C, Ay)
H = Midpoint(Ay, C)
text1: dAyC + ""
I = Midpoint(C, B)
J = Midpoint(C, ABxy)
K = Midpoint(B, E)
L = Midpoint(B, F)
M = Midpoint(B, D)
N = Midpoint(A, E)
O = Midpoint(E, Bx)
P = Midpoint(Bx, F)
Q = Midpoint(D, A)
R = Midpoint(Ay, D)
S = Midpoint(R, I)
T = Midpoint(ABxy, F)
U = Midpoint(I, T)
V = Midpoint(K, P)
W = Midpoint(Q, K)
Z = Midpoint(ABxy, Bx)
A_1 = Midpoint(Ay, ABxy)
dCABxy = Distance(ABxy, C)
text2: dCABxy + ""
dABxyAy = Distance(ABxy, Ay)
text3: dABxyAy + ""
dABxyF = Distance(ABxy, F)
dFBx = Distance(F, Bx)
dABxyBx = Distance(ABxy, Bx)
dCB = Distance(C, B)
dBE = Distance(B, E)
dFB = Distance(F, B)
dBD = Distance(B, D)
text4: dABxyF + ""
text5: dFBx + ""
text6: dABxyBx + ""
text7: dCB + ""
text8: dBE + ""
text9: dBD + ""
text10: dFB + ""
text13: dBD + " x " + dBE + " = " + poly4
text12: dCABxy + " x " + dABxyF + " = " + poly2
text14: dFB + " x " + dFBx + " = " + poly3
Poly: poly1 + poly2 + poly3 + poly4
text17: dABxyAy + " x " + dABxyBx + " = " + Poly
text18: poly1 + "+" + poly2 + "+" + poly3 + "+" + poly4
text19: "=" + Poly
m = false
n = false
o = false
text11: "" + dAyC + " x " + dCB + " = " + poly1 + ""

Tool: Complex Multiplication (command ComplexMultiplication)
Select Points at O(0, 0), P(0, -1), A and B for A*B
Input: O, P, A, B
Output: j, AB

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
b = Segment(O, A)
f = Segment(O, B)
G = Intersect(d, xAxis, 1)
g = Circle(D, P, G)
E = Intersect(g, yAxis, 2)
e = Circle(O, E)
a, h = AngularBisector(f, b)
D' = Mirror(D, a)
i = Ray(O, D')
AB = Intersect(e, i, 1)
j = Segment(O, AB)

Tool: Complex Division (command ComplexDivision)
Select Points O(0, 0), P(0, -1), A and B for A/B
Input: O, P, A, B
Output: l, C

A/B

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
e = AngularBisector(A, O, D)
B' = Mirror(B, e)
f = Ray(O, B')
E = Intersect(c, yAxis, 1)
F = Intersect(d, xAxis, 1)
g = Segment(F, E)
G = Midpoint(g)
h = OrthogonalLine(G, g)
i = Segment(P, F)
H = Midpoint(i)
j = OrthogonalLine(H, i)
I = Intersect(h, j)
k = Circle(I, F)
J = Intersect(k, xAxis, 2)
p = Circle(O, J)
C = Intersect(p, f)
l = Segment(O, C)

Tool: Complex Addition (command ComplexAddition)
Select Points O(0, 0), A and B for A + B
Input: O, A, B
Output: C', c

A + B

u = Vector(O, B)
C' = Translate(A, u)
c = Segment(O, C')

Tool: Complex Subtraction (command ComplexSubtraction)
Select Points O(0, 0), A and B for A - B
Input: O, A, B
Output: c, A'

A - B

u = Vector(B, O)
A'_1 = Translate(A, u)
A' = Translate(A, u)
c = Segment(O, A')