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Home > Fractal Pancakes
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"Sierpinski Sieve," a pancake by Nathan Shields (www.10minutemath.com)A Sierpinski triangle is a fractal, a structure that displays self-similarity at various scales. This fractal is created by recursively removing triangular pieces from the structure indefinitely - of course, the pancake isn't very hearty if you really do this, but you get the idea. To see about making your own fractal pancakes, as well as other topics I find interesting as a math teacher, check out my blog. --- Nathan Shields (www.10minutemath.com)
Jun 14, 2012
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"Pythagorean Tree," a pancake by Nathan Shields (www.10minutemath.com)This fractal, like many others, is fun to doodle at faculty meetings. Here, each triple of touching squares encloses a right triangle in a traditional visualization of the Pythagorean Theorem. To see about making your own fractal pancakes, as well as other topics I find interesting as a math teacher, check out my blog. --- Nathan Shields (www.10minutemath.com)Jun 14, 2012
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"Mandelbrot Set," a pancake by Nathan Shields (www.10minutemath.com)The Mandelbrot Set, which is one of the tastiest fractals, is the collection of points c on the complex plane which allow the iterated transformation z = z² + c to remain within a given threshold. I've always been awestruck by the infinite complexity that springs from that simple equation. To see about making your own fractal pancakes, as well as other topics I find interesting as a math teacher, check out my blog. --- Nathan Shields (www.10minutemath.com)Jun 14, 2012
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"Lorenz Attractor," a pancake by Nathan Shields (www.10minutemath.com)A Lorenz attractor comes from a system of three differential equations created to model convection in the atmosphere, and frequently used to show the sensitivity of a chaotic system to initial conditions. For another chaotic system, invite your kids to help design the pancakes. To see about making your own fractal pancakes, as well as other topics I find interesting as a math teacher, check out my blog. --- Nathan Shields (www.10minutemath.com)Jun 14, 2012
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The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius bands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.