Geometric pattern
I saw a nice pattern in Matt's t-shirt and I thought I can make it in GeoGebra:
https://www.youtube.com/watch?v=ga9Qk38FaHM&ab_channel=Stand-upMaths
The code is a little messy but works. I will refactor in the future. :)
If you like my work, you can support me in Patreon:
https://www.patreon.com/jcponce
Get my recent Mathematical Art with GeoGebra ebook:
https://www.patreon.com/jcponce/shop/mathematical-art-with-geogebra-577631
∞ Thanks fro your support!
GGB scripting version 1
A1 = (0, 0)
A2 = (x(A1) + 0.87, y(A1) + 0.5)
A3 = (x(A1) + 0.87, y(A1) + 3)
A4 = (x(A1), y(A1) + 3.5)
A5 = (x(A1) -0.87, y(A1) + 3)
A6 = (x(A1) - 0.87, y(A1) + 0.5)
rightSide = Polygon({A1, A2, A3, A4, A1})
leftSide = Polygon({A1, A4, A5, A6, A1})
rightSide' = Polygon({A1, A2, A3, A4, A1})
leftSide' = Polygon({A1, A4, A5, A6, A1})
block01 = {rightSide, leftSide}
block02 = Rotate(block01, 2pi/3, A1)
block03 = Rotate(block01, -2pi/3, A1)
block02' = Rotate(block01, 2pi/3, A1)
block03' = Rotate(block01, -2pi/3, A1)
centerFigure = {rightSide, leftSide, block02, block03}
#d1 = Length(A1, A4) + Length(A1, A2)
B1 = (x(A1) + 3.9, y(A1) + 2.25)
B2 = (x(A1), y(A1) + 4.5)
B3 = (x(A1) - 3.9, y(A1) + 2.25)
B4 = (x(A1) - 3.9, y(A1) - 2.25)
B5 = (x(A1), y(A1) - 4.5)
B6 = (x(A1) + 3.9, y(A1) - 2.25)
Execute(Zip("u"+k+" = Vector(A1, B"+k+")", k, 1...6))
#layer01 = Translate(centerFigure, u1)
Execute(Zip("layer0"+k+" = Translate(centerFigure, u"+k+")", k, 1...6))
Execute(Zip("layer0"+k+"' = Translate(centerFigure, u"+k+")", k, 1...6))
small01 = Rotate(Translate(block01, u2), -pi/3, B2)
small02 = Rotate(Translate(block01, u2), pi/3, B2)
small03 = Rotate(Translate(block01, u2), pi/3, A1)
small04 = Translate(Rotate(block01, pi/3, A1), u4)
small05 = Translate(Rotate(block01, pi, A1), u4)
small06 = Translate(Rotate(block01, pi, A1), u5)
small07 = Translate(Rotate(block01, pi, A1), u6)
small08 = Translate(Rotate(block01, -pi/3, A1), u6)
small09 = Translate(Rotate(block01, -pi/3, A1), u1)
small01' = Rotate(Translate(block01, u2), -pi/3, B2)
small02' = Rotate(Translate(block01, u2), pi/3, B2)
small03' = Rotate(Translate(block01, u2), pi/3, A1)
small04' = Translate(Rotate(block01, pi/3, A1), u4)
small05' = Translate(Rotate(block01, pi, A1), u4)
small06' = Translate(Rotate(block01, pi, A1), u5)
small07' = Translate(Rotate(block01, pi, A1), u6)
small08' = Translate(Rotate(block01, -pi/3, A1), u6)
small09' = Translate(Rotate(block01, -pi/3, A1), u1)
GGB scripting version 2
A1 = (0, 0)
A2 = (x(A1) + 0.87, y(A1) + 0.5)
A3 = (x(A1) + 0.87, y(A1) + 3)
A4 = (x(A1), y(A1) + 3.5)
A5 = (x(A1) -0.87, y(A1) + 3)
A6 = (x(A1) - 0.87, y(A1) + 0.5)
Ln = 1...6
Execute(Zip("SetVisibleInView(A"+k+", 1, false)", k, Ln))
rightSide = Polygon({A1, A2, A3, A4, A1})
leftSide = Polygon({A1, A4, A5, A6, A1})
SetLayer(rightSide, 4)
SetLayer(leftSide, 4)
rightSide' = Polygon({A1, A2, A3, A4, A1})
leftSide' = Polygon({A1, A4, A5, A6, A1})
SetLayer(rightSide', 5)
SetLayer(leftSide', 5)
block01 = {rightSide, leftSide}
block02 = Rotate(block01, 2pi/3, A1)
block03 = Rotate(block01, -2pi/3, A1)
SetLayer(block02, 4)
SetLayer(block03, 4)
block02' = Rotate(block01, 2pi/3, A1)
block03' = Rotate(block01, -2pi/3, A1)
SetLayer(block02', 5)
SetLayer(block03', 5)
centerFigure = {rightSide, leftSide, block02, block03}
B1 = (x(A1) + 3.9, y(A1) + 2.25)
B2 = (x(A1), y(A1) + 4.5)
B3 = (x(A1) - 3.9, y(A1) + 2.25)
B4 = (x(A1) - 3.9, y(A1) - 2.25)
B5 = (x(A1), y(A1) - 4.5)
B6 = (x(A1) + 3.9, y(A1) - 2.25)
Execute(Zip("SetVisibleInView(B"+k+", 1, false)", k, Ln))
Execute(Zip("u"+k+" = Vector(A1, B"+k+")", k, Ln))
Execute(Zip("SetVisibleInView(u"+k+", 1, false)", k, Ln))
Execute(Zip("first0"+k+" = Translate(centerFigure, u"+k+")", k, Ln))
Execute(Zip("first0"+k+"' = Translate(centerFigure, u"+k+")", k, Ln))
Execute(Zip("SetLayer(first0"+k+", 2)", k, Ln))
Execute(Zip("SetLayer(first0"+k+"', 3)", k, Ln))
Execute(Zip("second0"+k+" = Rotate(Translate(centerFigure, u"+k+"), pi/3, B"+k+")", k, Ln))
Execute(Zip("second0"+k+"' = Rotate(Translate(centerFigure, u"+k+"), pi/3, B"+k+")", k, Ln))
Execute(Zip("SetLayer(second0"+k+", 0)", k, Ln))
Execute(Zip("SetLayer(second0"+k+"', 1)", k, Ln))Final version
A1 = (0, 0)
A2 = (x(A1) + 0.87, y(A1) + 0.5)
A3 = (x(A1) + 0.87, y(A1) + 3)
A4 = (x(A1), y(A1) + 3.5)
A5 = (x(A1) -0.87, y(A1) + 3)
A6 = (x(A1) - 0.87, y(A1) + 0.5)
Ln = 1...6
Execute(Zip("SetVisibleInView(A"+k+", 1, false)", k, Ln))
rightSide = Polygon({A1, A2, A3, A4, A1})
leftSide = Polygon({A1, A4, A5, A6, A1})
rightSide' = Polygon({A1, A2, A3, A4, A1})
leftSide' = Polygon({A1, A4, A5, A6, A1})
block01 = {rightSide, leftSide}
block02 = Rotate(block01, 2pi/3, A1)
block03 = Rotate(block01, -2pi/3, A1)
block02' = Rotate(block01, 2pi/3, A1)
block03' = Rotate(block01, -2pi/3, A1)
centerFigure = {rightSide, leftSide, block02, block03}
B1 = (x(A1) + 3.9, y(A1) + 2.25)
B2 = (x(A1), y(A1) + 4.5)
B3 = (x(A1) - 3.9, y(A1) + 2.25)
B4 = (x(A1) - 3.9, y(A1) - 2.25)
B5 = (x(A1), y(A1) - 4.5)
B6 = (x(A1) + 3.9, y(A1) - 2.25)
Execute(Zip("SetVisibleInView(B"+k+", 1, false)", k, Ln))
Execute(Zip("u"+k+" = Vector(A1, B"+k+")", k, Ln))
Execute(Zip("SetVisibleInView(u"+k+", 1, false)", k, Ln))
Execute(Zip("first0"+k+" = Translate(centerFigure, u"+k+")", k, Ln))
Execute(Zip("first0"+k+"' = Translate(centerFigure, u"+k+")", k, Ln))
Execute(Zip("second0"+k+" = Rotate(Translate(centerFigure, u"+k+"), pi/3, B"+k+")", k, Ln))
Execute(Zip("second0"+k+"' = Rotate(Translate(centerFigure, u"+k+"), pi/3, B"+k+")", k, Ln))
C1 = (x(A1), y(A1) + 2.5)
C2 = (x(A1) + 0.87, y(A1) + 3)
C3 = (x(A1), y(A1) + 3.5)
C4 = (x(A1) - 0.87, y(A1) + 3)
Execute(Zip("SetVisibleInView(C"+k+", 1, false)", k, 1...4))
rom01 = Polygon({C1, C2, C3, C4})
rom02 = Rotate(rom01, 2pi/3)
rom03 = Rotate(rom01, -2pi/3)
Lk = {5, 6, 1}
Execute(Zip("p0"+k+" = Translate(rom01, u"+k+")", k, 1...3))
Execute(Zip("q0"+k+" = Translate(rom02, u"+k+")", k, 3...5))
Execute(Zip("r0"+k+" = Translate(rom03, u"+k+")", k, Lk))
Execute(Zip("p0"+k+"' = Translate(rom01, u"+k+")", k, 1...3))
Execute(Zip("q0"+k+"' = Translate(rom02, u"+k+")", k, 3...5))
Execute(Zip("r0"+k+"' = Translate(rom03, u"+k+")", k, Lk))
#-- Set Layers --#
Execute(Zip("SetLayer(second0"+k+", 0)", k, Ln))
Execute(Zip("SetLayer(second0"+k+"', 1)", k, Ln))
Execute(Zip("SetLayer(first0"+k+", 2)", k, Ln))
Execute(Zip("SetLayer(first0"+k+"', 3)", k, Ln))
Execute(Zip("SetLayer(p0"+k+", 4)", k, 1...3))
Execute(Zip("SetLayer(q0"+k+", 4)", k, 3...5))
Execute(Zip("SetLayer(r0"+k+", 4)", k, Lk))
Execute(Zip("SetLayer(p0"+k+"', 5)", k, 1...3))
Execute(Zip("SetLayer(q0"+k+"', 5)", k, 3...5))
Execute(Zip("SetLayer(r0"+k+"', 5)", k, Lk))
SetLayer(rightSide, 6)
SetLayer(leftSide, 6)
SetLayer(rightSide', 7)
SetLayer(leftSide', 7)
SetLayer(block02, 6)
SetLayer(block03, 6)
SetLayer(block02', 7)
SetLayer(block03', 7)