Epitrochoid
The parametric equation for one of the shapes associated with spirographs along with an example.
The variable “a” is the radius of the first circle that the second one “b” revolves around (think planets).
The “b” value is the radius of the circle on the outside that turns on the edge of the middle circle.
The variable T is kind of like the step. As the graph moves, the T controls how far the values are placed apart (i.e. you could have a straight line, skipping all the points in between, or you could plot the whole curve).
The variable “p” is the pen offset. When it is equal to “b”, the pen starts at the edge of the smaller circle.
Epitrochoid belongs to the following groups:
Art in Math, Globes, Spheres and Curves - 2 per day, Nerds Unite and Numbers One to a Trillion Available for sale asT-Shirts
Daniel Rayfield
cool work but no idea what it stands for ;)
Rowan
people ask how I make them…
well, there is the math behind it at least!
ECGardner
This is super cool, Rowan. It gave the science and math geek in me a huge smile. :)
MuscularTeeth
insanely cool !
Mui-Ling Teh
My gr.11/12 calculas teacher would love this. We played with graphing calcutors a lot in class and once had an assignment to create an image out of formulas like the one above. That was long ago; don’t remeber how they work now :P. My teacher was one of those really nerdy types who says stuff like “The formula for a hill is y=square root of x”. so he’d try to extract a formula for any shape; or challenge a student to figure what formula makes the shape. It was a good class; the assignment was pretty fun; we had to come up with a cheesy advertisement along with whatever we created :P.
Rowan replied
That sounds like a lot of fun! My gr 11/12 teachers would always say “so this is what you’ve been doing instead of your homework…”
thank you for the comment!
Stuart Cooney
That is so cool, Rowan—the beauty of maths!
LizVengeance
I need this for my final XD
jemimalovesbigted
my head hurts after reading your explanation! love the design though!! =P