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Wiki Tag: geometry

Fibonacci and the Golden Spiral

  • Author By kmaddox
  • Publication date April 17, 2025
Banner image for the Fibonacci and the Golden Spiral booth

The Fibonacci sequence can be seen throughout nature and the universe at varying angles. Fibonacci spirals are common natural occurrences that model this sequence. Videos: Video from NOVA about pi and the Fibonacci sequence: https://myarkansaspbs.pbslearningmedia.org/resource/nvmm-math-pifibonacci/pi-the-fibonacci-sequence/ Khan Academy video about calculations with the Fibonacci sequence: https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:sequences-and-series-ncert-new/xea4762213f311c5e:series/v/worked-example-fibonacci-sequence Additional Resources: Wikipedia article about the Fibonacci spiral: https://en.wikipedia.org/wiki/Golden_spiral…Continue Reading Fibonacci and the Golden Spiral

Using Computation to Self-Assemble Patterns

  • Author By kmaddox
  • Publication date April 10, 2024

Self-assembly is the process during which a collection of relatively simple components, starting in a disorganized state, autonomously combine into a more complex structure. During self-assembly, there is no external guidance or direction, and the self-assembling components experience only local interactions and typically obey a simple set of rules that govern how they combine. We…Continue Reading Using Computation to Self-Assemble Patterns

Ruled Hyperbolic Paraboloid

  • Author By kmaddox
  • Publication date April 10, 2024

This sculpture by Shalese Fitzgerald demonstrates the “ruling” of the hyperbolic paraboloid by lines. You can find other works by Fitz on instagram at @SFitzgerald_Art https://www.instagram.com/SFitzgerald_Art/ Additional Resources: An article describing how to create your own hyperbolic paraboloid: https://mathcraft.wonderhowto.com/how-to/make-hyperbolic-paraboloid-using-skewers-0131751/ An demonstration of hyperbolic paraboloids as ruled surfaces: https://demonstrations.wolfram.com/HyperbolicParaboloidAsARuledSurface/ A Wikipedia article about ruled surfaces: https://en.wikipedia.org/wiki/Ruled_surface…Continue Reading Ruled Hyperbolic Paraboloid

Kakeya Needle Problem

  • Author By kmaddox
  • Publication date April 10, 2024
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Given a needle (or stick), what is the smallest area shape that we need to rotate the needle 360 degrees? We will look at this problem from the perspective of several different shapes, we will start with a circle and slowly shave off parts of the shape to see that we can get smaller and…Continue Reading Kakeya Needle Problem

Experiencing Hyperbolic Geometry

  • Author By kmaddox
  • Publication date March 12, 2024

Experience mind bending hyperbolic geometry through virtual reality and craft activities. Come prepared to test your limits on reality with Hyperbolica, a virtual reality puzzle adventure game that visualizes what hyperbolic space is and how it can be interacted with. Then we will create a fun model of the hyperbolic plane to remember your time…Continue Reading Experiencing Hyperbolic Geometry

Platonic Solids

  • Author By kmaddox
  • Publication date March 10, 2024
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Platonic Solids are 3D shapes that: have faces identical in shape and size have the same number of faces meeting at each vertex, and are convex. How many such solids do you think meet these criteria? Surprisingly, there are precisely 5 and you can easily make them at home. With a hands-on approach through construction…Continue Reading Platonic Solids