Channel: PBS Infinite Series

Category: Education

Tags: haledimensionalinfinitemaths3dconjecturekelvinshapesdesignbeesenergyinfinite seriesefficiencybiologyinsectsstructuremarcus4dsquarehoneycombnumerologyseriesterentius varrosciencegeometrymathhexagonaldimensions

Description: Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: to.pbs.org/donateinfi Be sure to check out It's OK to be Smart's video on nature's love of hexagons youtu.be/Pypd_yKGYpA And try CuriosityStream today: curiositystream.com/infinite Use the promo code: infinite The image of the 3D honeycomb sheet used at 7:33 and within the thumbnail image is a recolored/modified version of Andrew Kepert's "Tesselation of space using truncated octahedra." commons.wikimedia.org/wiki/File:Truncated_octahedra.jpg The original of this image is used again at 8:33 and 9:29. The images of the Weaire-Phelan Structure, the truncated Hexagonal Trapezohedron and the Pyritohedron at 9:14 were created by Tomruen, links below: commons.wikimedia.org/w/index.php?curid=10471229 commons.wikimedia.org/w/index.php?curid=17024143 en.wikipedia.org/wiki/Weaire%E2%80%93Phelan_structure#/media/File:Irregular_dodecahedron.png Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Why Computers are Bad at Algebra youtube.com/watch?v=pQs_wx8eoQ8 Why is there a hexagonal structure in honeycombs? Why not squares? Or asymmetrical blobby shapes? In 36 B.C., the Roman scholar Marcus Terentius Varro wrote about two of the leading theories of the day. First: bees have six legs, so they must obviously prefer six-sided shapes. But that charming piece of numerology did not fool the geometers of day. They provided a second theory: Hexagons are the most efficient shape. Bees use wax to build the honeycombs -- and producing that wax expends bee energy. The ideal honeycomb structure is one that minimizes the amount of wax needed, while maximizing storage -- and the hexagonal structure does this best. Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (kornhaberbrown.com) Resources: Nature paper nature.com/news/how-honeycombs-can-build-themselves-1.13398#/b1 Hales’ proof of honeycomb conjecture: arxiv.org/pdf/math/9906042.pdf Older article on honeycomb conjecture ams.org/journals/bull/1964-70-04/S0002-9904-1964-11155-1/S0002-9904-1964-11155-1.pdf Overview of proof of honeycomb conjecture maa.org/frank-morgans-math-chat-hales-proves-hexagonal-honeycomb-conjecture npr.org/sections/krulwich/2013/05/13/183704091/what-is-it-about-bees-and-hexagons Kelvin -- soft-matter.seas.harvard.edu/images/1/17/Kelvin_Cell.pdf slate.com/articles/health_and_science/science/2015/07/hexagons_are_the_most_scientifically_efficient_packing_shape_as_bee_honeycomb.html