Those Fabulous Hexagons - Cornell UniversityThose Fabulous Hexagons Charlie Van Loan 5130 Upson...
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Those Fabulous Hexagons Charlie Van Loan 5130 Upson 1:30-2:30 Bring A Child To Work
Transcript of Those Fabulous Hexagons - Cornell UniversityThose Fabulous Hexagons Charlie Van Loan 5130 Upson...
ThoseFabulousHexagons
Charlie Van Loan5130 Upson1:30-2:30
Bring A ChildTo Work
Yes! No!
STOP
6 Sides 8 Sides
STOP
Hexagon Octagon
Hexagon Examples
How To Make a Nice Hexagon
Draw Six Dots
How To Make a Nice Hexagon
Nope!
Draw Six Dots and
Connect Them
How To Make a Nice Hexagon
Nope!
Draw Six Dots and
Connect With Six Lines
4
6
3
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How To Make a Nice Hexagon
Yes!
Draw Six Dots and
Connect With Six Lines
That Don’t Cross
Hexagonal Shapes in Nature
Artistic Useful
Can You Make One of These?
This Guy Can!
Strong and Economical
Strong and Economical
Strong and Economical
The Hex Nut
Biggest Hex Nuts On Campus
Where?
Biggest Hex Nuts On Campus
Turning Hex Nuts
Adjustable Crescent Wrenches
Allen Wrenches and Allen Screws
Hexagonal Hole
Pent Nuts: Making it Hard
Only the Fire Departmenthas the special wrench
Making A Perfect Hexagon
Examples of Perfect Polygons
Triangle
Pentagon
Square
Hexagon
Decagon
Octagon
Dodecagon
Important Word
A polygon is a shape with straight sides.
A 4-gon is a squareAn 6-gon is a hexagonAn 8-gon is an octagonA 1000-gon would look almost like a circle
The All-Important Prefix
5: Pentagon6: Hexagon7: Septagon*8: Octagon9: Nonagon10: Decagon
5: July6: August7: September8: October9: November10: December
Think ofMarch as theFirst Month
*Actually the preferred term is “Heptagon” , but that wrecks the analogy!
The All-Important Prefix
5: Pentagon6: Hexagon7: Septagon8: Octagon9: Nonagon10: Decagon
5: Pentember6: Hexember7: September8: October9: November10: December
“Star” Polygons
“Star” Polygons
Polygon Activity: Tiling
You Can Tile With Triangles
You Can Tile With Squares
You Cannot Tile with Pentagons
They do not fit together!
You Can Tile With Hexagons
How many different colors do we need so each tile is
different from its neighbors?
7 !
Little Question Big Answer
About how many little hex tiles do you need to tile the Earth?
(a) 1,000,000(b) 1,000,000,000(c) 1.000,000,000,000,000(d) 1,000,000,000,000,000,000
Tiling with Hexagons and Triangles
Tiling with Octagons and Squares
An Important Word
It is possible to tessellate the plane with hexagons.
It is possible to tessellate the plane with squares and octagons
Another Polygon Activity: Making Perfect Solids
There are only 5 Perfect (Platonic) Solids
Dodecahedron
12 faces
Each face is a perfect pentagon
Archimedean Solids
The Most Famous Archimedean Solid
??? Hexagons
??? Pentagons
The Most Famous Archimedean Solid
22 Hexagons
12 Pentagons
Why I Like Hexagons
1. I like artistic things. Hexagons are nice to look at.
2. I like building things. Hexagons are useful.
I like Engineering
GreatAnimal Engineers
Great Animal Engineers
Great Animal Engineers
Geometry Is Important
How do you fit all this stuff inside?
Computers Help
Can’t keep track of everything in our heads!
Geometry is Important
How to you get fromA to B?
Build Beautiful Things…
And Learn to Find Them
Why Do I Like Hexagons?
The REAL reason is this….
My Favorite Candy Is Hexagonal
Recipe forSuccess
They Taste Better This Way
Become A True Hexagon Person!
![Primitive flag-transitive generalized hexagons and …0704.2845v2 [math.CO] 14 Mar 2008 Primitive flag-transitive generalized hexagons and octagons Csaba Schneider Informatics Research](https://static.fdocuments.us/doc/165x107/5b02cb537f8b9a2e228b6aa4/primitive-ag-transitive-generalized-hexagons-and-07042845v2-mathco-14.jpg)
