GeoGebra Classroom

# Spinning cube - Belt Trick

## GIF

Animation inspired by Jason Hise: Belt Trick and Pixelated_Donut Also check: The Strange Numbers That Birthed Modern Algebra Warning: The interactive demo is laggy. Download for better performance.

## Script

# A spinning cube with attached ribbons returns # to its original state only after two full turns, # rather than one turn. Four-dimensional numbers # called quaternions behave similarly, as do matter # particles such as electrons and quarks. # https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ speed = 1 α = Slider(0°, 360°, 1°, speed, 200) C = (cos(α), sin(α), 0) # Auxiliary functions #T(x, y, z) = pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) CrossX(x, y, z) = y * z(C) - z * y(C) CrossY(x, y, z) = z * x(C) - x * z(C) CrossZ(x, y, z) = x * y(C) - y * x(C) Dot(x, y, z) = x * x(C) + y * y(C) + z * z(C) KX(x, y, z) = ( x * x(C) + y * y(C) + z * z(C) ) * x(C) KY(x, y, z) = ( x * x(C) + y * y(C) + z * z(C) ) * y(C) KZ(x, y, z) = ( x * x(C) + y * y(C) + z * z(C) ) * z(C) PMinusKX(x, y, z) = ( x - KX(x, y, z) ) * cos( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) PMinusKY(x, y, z) = ( y - KY(x, y, z) ) * cos( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) PMinusKZ(x, y, z) = ( z - KZ(x, y, z) ) * cos( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) PCrossCX(x, y, z) = CrossX(x, y, z) * sin( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) PCrossCY(x, y, z) = CrossY(x, y, z) * sin( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) PCrossCZ(x, y, z) = CrossZ(x, y, z) * sin( pi / ( 1 + exp(sqrt( x^2+y^2+z^2) - 9 ) ) ) RX(x, y, z) = KX(x, y, z) + PMinusKX(x, y, z) - PCrossCX(x, y, z) RY(x, y, z) = KY(x, y, z) + PMinusKY(x, y, z) - PCrossCY(x, y, z) RZ(x, y, z) = KZ(x, y, z) + PMinusKZ(x, y, z) - PCrossCZ(x, y, z) # Curves c1 = Curve( RX(cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t), 0), RY(cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t), 0), RZ(cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t), 0), t, 0, 1) c2 = Curve( RX(0, cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t)), RY(0, cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t)), RZ(0, cos(2pi * t)+20*tanh(9*cos(2pi * t)), sin(2pi * t)), t, 0, 1) c3 = Curve( RX(sin(2pi * t), 0, cos(2pi * t)+20*tanh(9*cos(2pi * t))), RY(sin(2pi * t), 0, cos(2pi * t)+20*tanh(9*cos(2pi * t))), RZ(sin(2pi * t), 0, cos(2pi * t)+20*tanh(9*cos(2pi * t))), t, 0, 1) # Cube s = 2.5 A1 = (s, s, -s) A2 = (-s, s, -s) A3 = (-s, -s, -s) cube = Rotate(Cube(A1, A2, A3), 2*α, zAxis)