As an outcome of watching a child’s video, I formerly composed a brief item around the “corners” of a circle. The video was designed to teach children the miscellaneous shapes—exactly how many kind of sides does a form have, and exactly how many kind of corners?
The video kept a circle has actually no corners. I called that right into question. I still do. And yet, I perform not. I currently think it’s all in exactly how you look at it. Or, you might say, it’s all in the mathematical perspective. Consider.
You are watching: Why is a circle not a polygon
The Circle by Definition
One can define the two-dimensional circle as the complete collection or “set” of points equifar-off from a collection suggest, not part of the circle. In effect, a circle is like a symmetrically exploded suggest.1 Because it takes at least 3 points to develop a edge, by derivation in this fashion, some say the circle has actually no corners. But is that the finish of the discussion?
Circle a Polygon? By the Method of Limits
One deserve to visualize a circle through the procedure of incrementally including sides to a continual polygon. A triangle becomes a square; the square becomes a pentagon; the pentagon becomes a hexagon; the hexagon becomes a heptagon; the heptagon becomes an octagon; and so on.
Overcoming a Contradiction
Even if it could be completed, the variety of sides would certainly be unlimited, rather than zero. Tbelow are 2 ways roughly this that I can come up via. Option one: it can be asserted that a true circle deserve to never be completed making use of the technique of limits. Therefore, a circle is not a polygon.
However before, tbelow is a snag to such a supposition: it says the approach of borders is not strictly legit for various other applications. Yet the principle of boundaries is the basis for the Calculus. Rather than follow this line of thinking, perhaps it is much better to take on option 2. Ignore the totality worry.
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My last take on the matter is that mathematicians must take stock on reality. Math is just a tool. It, like computer systems or even words, is not an end in itself, just a tool. To say a polygon of ever before raising sides never makes it to a true circle is short-sighted. A circle is a polygon that has actually had actually its variety of sides boosted over endmuch less time. It made it!
1 If one might say a suggest is “round”.
Note: You might likewise gain Point on a Line, a Line on a Plane, and also a Plane in Space