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Quarks, Protons, Neutrons, Electrons, and almost all building blocks are circles, and all circles are a perfect 360 degrees throughout the circumference. In which, angles; the bending place of 2 rays that lead off to define the existence of shapes, are one of the absolute last and smallest pieces in Universal existence. Some of these facts are all about angles; uses, pieces, equations, and degree measures.

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- In geometry and trigonometry, an angle is the figure formed by two rays sharing a common endpoint. The endpoint is called the vertex of the angle.
- The magnitude of the angle is the "amount of rotation" that separates the two rays.
- The word “angle” comes from the Latin word “angulus”, meaning; "a corner."
- In order to measure an angle θ, a circular arc centered at the vertex of the angle is made.
- The value of θ thus defined is independent of the size of the circle.
- In many geometrical situations, angles that differ by an exact multiple of a full circle are effectively equivalent.
- However, when tracing a curve such as a spiral using polar coordinates, an extra full turn gives rise to a quite different point on the curve.
- Angles are considered dimensionless, since they are defined as the ratio of lengths.
- The degree, is 1/360 of a full circle, so one full circle is 360 degrees.
- The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius.
- The full circle is one complete revolution. The revolution and rotation are abbreviated “rev” and “rot”.
- The right angle is 1/4 of a full circle.
- The angle of the equilateral triangle is 1/6 of a full circle.
- The grad, also called grade, gradian, or gon is 1/400 of a full circle.
- The point, used in navigation, is 1/32 of a full circle.
- The astronomical hour angle is 1/24 of a full circle.
- The binary degree, a.k.a. the binary radian or “brad”, is 1/256 of a full circle.
- The grade of a slope, or gradient, is not truly an angle measure. Instead it is equal to the tangent of the angle, or sometimes the sine.

The angle exists to define shape, without it, all would be liquid... or gas... or plasma I don’t really know, so be glad you learn this, it’s essential for everything building!

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By: PRO-Fessor E=MineCraft2

**The Bees Portfolio**

Cover Letter

The “Do Bees Build it Best” unit… all about geometry. We have studied the functions of geometrical patterns, and the natural shapes in our world. We have looked into tessellations to find what geometric shapes actually do fit together. We have looked into Pythagorean Theorem to to find angles and get lengths of triangle sides. Along with trigonometry, which we used to angles to find lengths and ratios. Throughout this unit, our goal was to the unit’s title... the question: “Do Bees Build it Best”? And by that, we wanted to know why they use hexagons to shape up their hives. Using our terms, we tested through many practices and a whole graph of data to find out about how perimeter effects area more that seemingly so. We found that circles actually have the most area out of all shapes even if for say a triangle had even if both had a perimeter of for instance 100. So when it comes to area and perimeter, circles stand on one end, triangles on the other. We also had to know the fact- only 3 shapes tessellate... triangles, squares, and hexagons and that’s it. Circles don’t tessellate, so you’d have a wasted space with gaps. Since bees wanted more honey to store, but organized well in each cell, the fact that hexagons tessellate, and are closer to circles than triangles and squares, bees use hexagons to get the most possible honey out of a cell, with no cell gaps, and perfectly tessellate-able shapes.

My Experience

I definitely didn’t know what the title of this unit what supposed to mean, but I had a distinct feeling it had something to do with Geometry. I definitely got a useful and fresh refresh with surface area, volume, area, and Pythagorean Theorem. Trigonometry was a bit difficult to comprehend immediately, but it seemed more simple once I had some practice. Once we solved the reason for the title of our first POW- the Bee Research, which was all about why do bees use hexagon cells, it seemed like a sudden point where man is actually the simplest creature on the planet.

Extension Question

As an extension question I still wonder... how the hectical hecks did those scientists before calculators know what the sine cosine and tangent of the lengths were? It’s like finding the square root of 53... which leads me to when was trigonometry first used?