Someone Drawing a Perfect Circle
Funny you asked this question, I'k publishing a newspaper proving that perfect circles do non exist...anywhere. Circles are made from right triangles.....the equation to calculate Pi based on the number of triangles (or number of sides to a circle is..... f(10)= xsin(Pi/10) In this equation x= the number of sides to a circle. Every bit 10 approaches infinity, f(x) will approach pi. If yous accept a graphing calculator, graph this equation and you will encounter it works. I drew several 'circles' with right triangles to testify how when you clasp more and more triangles (or polygons, which are made from triangles) within a perimeter you go closer and closer to a 'perfect circle' simply you never reach it...here is a quick explanation. In this drawing Jason Padgett is showing how perfect circles do non exist...anywhere in the universe. Circles are made from triangles as are all shapes and are deeply interconnected with the number Pi. The more than trianlges you squeeze within a certain perimeter the closer and closer you approach a circumvolve simply you never attain it...yous only get closer and closer. This is WHY Pi goes to infininty. Pi is the circumference of a circle (how far around the perimieter) divided by its diameter (the distance from 1 side of the circle through the center and to the other side). When you add more triangles, the circumference gets slightly larger each time y'all add more triangles (simply by an ever decreasing amount), only the diameter stays the aforementioned. A circle with 180 triangles when you split it's circumference by it diameter you lot get 3.141433 (Pi accurate to three decimals). A circle with 360 right triangles, one right triangle every ane degree, gives yous 3.141552 (Pi accurate to 4 decimals). This motion picture is 720 right triangles, which when you divide it's circumference by information technology's diameter gives you lot 3.141582 (Pi still accurate to four decimals but almost to five). If we could draw a circle with 25,000 right triangles (and nature does this and far more everday) information technology would exist 3.141592645 (Pi accurate to seven digits). What is so amazing virtually Pi is that everything in the universe breaks downwardly into it. All shapes (icluding circles, and 'perfect circles' don't actually be..their fabricated from triangles) suspension down into direct lines and triangles. Every curve breaks downwardly into microscopic straight lines that modify angle past very small amounts (simply similar this picture looks similar a curve but is all perfectly straight lines). In math (trigonemetry) they teach how to convert measurements made in degrees (360 degrees is a circumvolve), into measurements made with Pi (this measurement is chosen Pi radians). To convert degrees into Pi radians yous multiply the degrees past Pi/180 (the fraction of pi over 180). All directly lines are 180 degrees (two right triangles make a directly line 90 + 90 =180) and every ttriangle that exists when you add up all iii inner angles e'er equals 180 degrees (the same as the straight line). Since all shapes that exist break down into straight lines and triangles lets see what happens when we convert the degrees into Pi radians. 180 times Pi/180= 180Pi/180 (in words 180 times pi divided by 180). The 180's cancel out because 180 divided by 180 equals one and one times Pi equals Pi! So every shape in the universe breaks down into pieces of Pi, literally. And some say nature doesn't have a humor! This picture is fatigued with straight lines only. It is 720 right triangles rotating ane/2 caste at a time. There is no curve but every bit y'all can see the more triangles that are sqeezed into the perimeter the more it APPEARS to be a circle or bend. Just similar when yous look at a mountain and think, that is not a curve or circumvolve, but if you zoom out into outerspace and look at the earth information technology LOOKS like a perfect sphere. Merely when you're on the world it looks completely dissimilar. In other words, what is a circle is relative. The mountain is not a circle when you lot're looking at information technology ane the world, but it looks like a circle (or part of one) from outspace. This is i of the many beautiful illusions of relativity. For those who similar the equation aspect, graph f(x)=xsin(Pi/10) and see what happens. As x (the number of sides to a circle) approaches infinity, f(ten) will approach Pi. Final but nearly important is that we accept 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 chosen a Planck length. Information technology was discovered past Maxwell Planck and he won the nobel prize for it. Information technology'south accepted 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 can keep adding triangles only until each "side" to the circumvolve (microscopic sides) equals one Planck length and this is where Pi physically ends without question. The reason mathematicans have missed this (I recollect) is because of the lack of viewing math from a purely creative (pure geometry) bespeak of view. When you lot practice equations of circles you never see with your own eyes like yous do when you await at this drawing. We are visual creatures and like they say, a picture is worth a thousand words, or in this case, a thousand meg equations. 1 pic shows visually what most would never find in an equation solitary.
Source: https://www.answerbag.com/q_view/704347
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