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Tetrahedrons What are they and how do we use them?

Tetrahedrons What are they and how do we use them?. Courtney Shafer and Mellissa Toothman. What is a tetrahedron?. Let’s think about the word tetrahedron. What do you think it means?. The word- Tetrahedron. The word tetrahedron can be broken into 2 parts: tetra and hedron Tetra means:

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Tetrahedrons What are they and how do we use them?

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  1. Tetrahedrons What are they and how do we use them? Courtney Shafer and Mellissa Toothman

  2. What is a tetrahedron? • Let’s think about the word tetrahedron. • What do you think it means?

  3. The word- Tetrahedron • The word tetrahedron can be broken into 2 parts: tetra and hedron • Tetra means: four • Hedron means: a crystal or geometric figure having a specific kind or number of surfaces. Make sense yet????

  4. Put it all together… • When you put all of that together you get the full definition for what a tetrahedron actually is : • A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. Based on a pyramid shape and is the strongest structure known.

  5. What does a tetrahedron look like??

  6. Let’s make our own tetrahedron. Make a Tetrahedron from a Small Envelope • Here is a simple way to make a tetrahedron from a small envelope. • All you need is a small envelope, a ruler, a pencil and scissors.

  7. Instructions • Open the flap of a small envelope. • Using a ruler and a pencil, mark the diagonal lines from each corner to the opposite corner. • Mark a third vertical line through the middle of the envelope. • Fold along each of the lines.

  8. Then… • Cut along the top two "V"-shaped lines (discard the top of the envelope).

  9. Next… • Open up the envelope, flattening the bottom a bit. • Tuck one side of the envelope into the other side.

  10. And Finally… • You have a tetrahedron! • To decorate it: untuck it, draw on the sides (but not on the tucked-in side), then re-tuck one side in.

  11. Now what??? • Now we have discussed what a tetrahedron is, made an example, and know about all of it’s characteristics. • Let’s talk about how we can use tetrahedrons.

  12. But first, some history… • It is part of Bell's legend that he made his most important discoveries on accident. • The telephone was an accidental invention that came from the telegraph! • The tetrahedron grew out of his search for a flying machine.

  13. A kite?!?! • Bell hoped to develop a kite large enough to carry a man. • How could he increase the size without increasing the weight? • With this question, Bell took his first step on the road to the tetrahedron .

  14. His first innovation was the triangular box kite.

  15. Bell removed sides which decreased the weight of the kite. • Moreover, a triangle is a more stable shape than a rectangle, which tends to distort in the wind.

  16. The next step was to combine several small triangular kites. • By adding many small surfaces, Bell increased the total surface area, with little increase in weight.

  17. Eventually, he evolved a figure made up of four equilateral triangles. • This was the tetrahedron, one of nature's most stable structures. • His invention looked something like this…

  18. Bell’s kite’s are now displayed for the public to view. • The kite’s are on display in Baddeck, Nova Scotia.

  19. What does all of this mean? • Bell had trouble constructing the flying machine for many reasons. • One of which being the materials he was using were taking up too much space. • The amount of space an object takes up is called it’s surface area.

  20. Surface area of a tetrahedron… • It’s not too hard, you just have to remember this formula: b= base h=height a= area of a side 2

  21. Get out your calculator!!!!! • Here are some example problems. • Work with a partner to try and figure our what the surface area would be for these tetrahedrons. Example 1- b=8 cm, h=4 cm, and a=10 cm Example 2- b=5 cm, h=6 cm, and a= 12 cm

  22. What else??? • What else can we do with a tetrahedron? • What other things are shaped like or have similar design to that of a tetrahedron?

  23. The Tetra-Harp

  24. The Silicate Model

  25. Dice

  26. Some diamonds and crystals

  27. What factors do you think will affect your kite’s chances of flying?

  28. Bell’s Challenge • Now… we are going to construct and actually FLY a tetrahedron kite!!!!

  29. Outcomes • Did your kite fly? • What outside elements affected your kite’s flight? • What could you have done differently?

  30. http://www.citerawv.us/resources/index.htm The End

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