Can You Draw a Perfect Circle Song

Funny you asked this question, I'thou publishing a newspaper proving that perfect circles do non exist...anywhere. Circles are fabricated from right triangles.....the equation to calculate Pi based on the number of triangles (or number of sides to a circle is..... f(x)= xsin(Pi/x) In this equation x= the number of sides to a circle. Equally 10 approaches infinity, f(10) will approach pi. If you take a graphing calculator, graph this equation and you will see information technology works. I drew several 'circles' with right triangles to testify how when you squeeze more and more triangles (or polygons, which are made from triangles) within a perimeter you get closer and closer to a 'perfect circumvolve' but you never accomplish it...here is a quick explanation. In this cartoon Jason Padgett is showing how perfect circles do not exist...anywhere in the universe. Circles are made from triangles as are all shapes and are securely interconnected with the number Pi. The more trianlges you clasp within a certain perimeter the closer and closer you arroyo a circumvolve only you never achieve information technology...you just become closer and closer. This is WHY Pi goes to infininty. Pi is the circumference of a circle (how far effectually the perimieter) divided past its bore (the altitude from one side of the circle through the center and to the other side). When you add more than triangles, the circumference gets slightly larger each time you add together more triangles (just by an e'er decreasing amount), but the diameter stays the same. A circumvolve with 180 triangles when you divide it'south circumference by it diameter y'all get 3.141433 (Pi accurate to three decimals). A circle with 360 right triangles, i right triangle every one degree, gives you 3.141552 (Pi authentic to iv decimals). This picture is 720 right triangles, which when yous divide it's circumference by it'due south diameter gives you 3.141582 (Pi still accurate to four decimals only almost to five). If we could draw a circumvolve with 25,000 right triangles (and nature does this and far more than everday) it would be iii.141592645 (Pi accurate to seven digits). What is and then amazing almost Pi is that everything in the universe breaks downward into it. All shapes (icluding circles, and 'perfect circles' don't actually exist..their made from triangles) intermission downwards into straight lines and triangles. Every curve breaks down into microscopic directly lines that change angle by very small amounts (just like this picture looks similar a bend simply is all perfectly straight lines). In math (trigonemetry) they teach how to convert measurements made in degrees (360 degrees is a circle), into measurements fabricated with Pi (this measurement is called Pi radians). To catechumen degrees into Pi radians y'all multiply the degrees by Pi/180 (the fraction of pi over 180). All direct lines are 180 degrees (two right triangles make a straight line 90 + ninety =180) and every ttriangle that exists when you add up all three inner angles always equals 180 degrees (the same as the straight line). Since all shapes that exist intermission downward into straight lines and triangles lets see what happens when nosotros convert the degrees into Pi radians. 180 times Pi/180= 180Pi/180 (in words 180 times pi divided past 180). The 180'southward cancel out because 180 divided by 180 equals one and one times Pi equals Pi! And then every shape in the universe breaks down into pieces of Pi, literally. And some say nature doesn't have a sense of humor! This motion picture is drawn with direct lines simply. It is 720 right triangles rotating 1/two degree at a time. In that location is no curve but equally y'all tin see the more triangles that are sqeezed into the perimeter the more it APPEARS to exist a circle or curve. But like when you look at a mountain and recall, that is not a curve or circle, simply if you zoom out into outerspace and look at the earth it LOOKS like a perfect sphere. But when yous're on the earth it looks completely different. In other words, what is a circumvolve is relative. The mountain is not a circle when you lot're looking at it i the earth, but it looks like a circumvolve (or part of 1) from outspace. This is one of the many beautiful illusions of relativity. For those who like the equation aspect, graph f(ten)=xsin(Pi/10) and see what happens. As x (the number of sides to a circle) approaches infinity, f(10) will arroyo Pi. Last merely nearly important is that we have been taught that Pi never ends. That is true when looking at this in pure equation form...but it is wrong when looking at a 'circle' in reality. This is the actually amazing part....Pi ends (physically). The smallest measurement in the universe is something called a Planck length. It was discovered past Maxwell Planck and he won the nobel prize for information technology. It's accustomed and used worldwide by mathematicians, nuclear physicists etc. What this means is that you cannot physically add an infinite number of triangles in a 'circle'. You tin keep calculation triangles just until each "side" to the circle (microscopic sides) equals one Planck length and this is where Pi physically ends without question. The reason mathematicans take missed this (I remember) is because of the lack of viewing math from a purely creative (pure geometry) signal of view. When you do equations of circles y'all never run into with your own eyes similar y'all do when you look at this drawing. We are visual creatures and like they say, a picture is worth a one thousand words, or in this example, a thousand million equations. I moving-picture show shows visually what well-nigh would never observe in an equation lonely.

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Source: https://www.answerbag.com/q_view/704347

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