Imp 2 Bees Portfolio

Topics: Hexagon, Regular polygon, Tessellation Pages: 4 (1329 words) Published: February 10, 2013
Introduction

When we think of bees, what do we think of? Do we think about getting stung? The sweet honey that they make? What about their crazy mathematical genius? Bees have, somehow, figured out that they should use hexagons for their honeycombs. How? I hove no clue- do I look like an apiologist to you? No. But I do know that the method the bees use is the best method for their intent.

The unit “Do Bees Build It Best?” helped me realize and confirm the previous. I studied geometry for the past two months- believe me; I know what I’m doing. To be able to make that statement, I studied the area and perimeter of all polygons, trigonometry, inverse trigonometry, and volume of surface area of three dimensional shapes. I did all of that just to find an answer. And bees really do build it best.

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Tessellation

Tessellation is everywhere in our world. Its on the bees honeycombs. On our floors. Mosaics are tessellations. On the quilts we curl up under on movie night. Often times, tessellations are just such a natural part of our lives that we don’t even notice the tessellations. A brick wall is a tessellation. Corn on the cob tessellates. Just look around- tessellations are everywhere!

But to tessellate, shapes have to have certain properties. The shapes in a mathematical, geometric tessellation need to be congruent. The tessellated shape cannot overlap or leave gaps, and the shape should be a polygon. Lastly, the vertices should look similar.

Some regular polygons, normal as they are, do not tessellate. Pentagons don’t tessellate, and neither do octagons. They overlap or leave gaps. And, looking at the rules listed in the previous paragraph, it is obvious that they don’t tessellate.

Three Dimensional Objects

Rectangular prisms are quite honestly the easiest part of geometry. Their surface area and volume are simple to discover. You simple use the following equation: 2LW + 2HW + 2LH....