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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

Tetrahedrons What are they and how do we use them?

Courtney Shafer and Mellissa Toothman

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

put it all together
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.
let s make our own tetrahedron
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.
instructions
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.
slide8
Then…
  • Cut along the top two "V"-shaped lines (discard the top of the envelope).
slide9
Next…
  • Open up the envelope, flattening the bottom a bit.
  • Tuck one side of the envelope into the other side.
and finally
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.
now what
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.
but first some history
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.
a kite
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 .
slide15
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.
slide16
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.
slide17
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…
slide19
Bell’s kite’s are now displayed for the public to view.
  • The kite’s are on display in Baddeck, Nova Scotia.
what does all of this mean
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.
surface area of a tetrahedron
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

get out your calculator
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

what else
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?
bell s challenge
Bell’s Challenge
  • Now… we are going to construct and actually FLY a tetrahedron kite!!!!
outcomes
Outcomes
  • Did your kite fly?
  • What outside elements affected your kite’s flight?
  • What could you have done differently?
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