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# Math of Honeycombs

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by

## Rahul Sethi

on 21 August 2016

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#### Transcript of Math of Honeycombs

Math of Honeycombs
The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter
REGULAR
HEXAGONS
A HEXAGON HAS 6 SIDES
DO YOU KNOW SOMETHING THAT HAS INFINITE SIDES?
A HEXAGON CAN BE BROKEN DOWN TO 6 CONGRUENT EQUILATERAL TRIANGLES
WHAT CAN YOU SAY ABOUT SYMMETRY IN A HEXAGON?
AREA OF A HEXAGON

If a polygon is REGULAR, all its sides are equal
BEFORE MOVING ON, LET'S HAVE A LOOK AT THE AREA-PERIMETER RATIOS FOR A FEW
"WELL-KNOWN" FIGURES
Why are honeycombs hexagonal?
Why do honeybees use HEXAGONAL structures? That too, REGULAR hexagons? Don't stress your brain, let us explain.
What exactly, can be called as a hexagon?
THIS FIGURE that
you're looking at
right now
Polygon (closed figure)
6 sides
6 interior angles (obviously)
HOW TO MAKE ONE RIGHT NOW
INTERIOR ANGLES?
HAVE A LOOK AT THE ANGLES
CELLS IN A HONEYCOMB
WAX
TO KNOW WHY WAX IS SO PRECIOUS, WE
SHOULD KNOW WHAT MAKES UP WAX...
Honeybees ingest honey to make beeswax. It takes approximately 8 kg of honey to produce 1 kg of wax. When the wax leaves the bee's body and comes in contact with the air, it causes the wax to solidify into dinner-plate shaped flakes. Then bees carefully mold the wax into the perfect honeycomb structure
#TooMuchInfo
AFTER DOING SOME MATH, YOU'LL REALIZE THAT ITS THE GREATEST FOR REGULAR HEXAGONS

HEXAGONS GIVE THE MOST AREA FOR A UNIT LENGTH OF WAX WALL. HENCE, THEY ARE PREFERRED.
THE HONEYCOMB CONJECTURE
YES, HE'S THE ONE
THOMAS HALES
THANKS FOR BEING A PART OF THE
COURSE ON ARCHITECTURAL DESIGN
BY UC 'BEE'RKELEY
3D Structure of a honeycomb cell

YES, FINALLY, IT'S OVER. THANKS FOR YOUR UNDIVIDED ATTENTION
#MitosisPuns :P #BIO
Working
Area of hexagon=
Full transcript