(see “TrollMath: Pi” link below…)
nice fractal but no one has succeeded in squaring a circle!
remember: the very existence of a fractal is based on an impossible premise: that one can write with an infinitely small pencil…
also there is no limit that the equation that describes the perimeter of the fractal approaches: the equation is p=4, ad infinitum. the box around the circle (the fractal) never can approach the circle itself.
further comments from the facebook share…
Arthur Frohlich the reason it doesn’t work is because as the fractal gets infinitely close to the close it becomes a squiggly line going around the edge of the circle instead of the solid line that the circle is made of. the extra distance is stored in the squiggles. great fractal though.
3 hours ago · Unlike · 1
- Arthur Frohlich also I’m pretty sure that if you continue that fractal it come out as an octagon or diamond not a circle.
3 hours ago · Like
- Jerry Hill that “extra distance” that is “stored in the squiggles” and is unvarying means that the fractal never can get “infinitely close[r] to the [circle]…”
about an hour ago · Like
- Jerry Hill that’s what i meant with the comment about no limit that the equation approaches
about an hour ago · Like
- Jerry Hill ”infinitely close” can never exist because that would involve an undefined operation–that’s why limits exist…
53 minutes ago · Like
- Jerry Hill all that said, kudos, @Arthur Frohlich for the phrase “stored in the squiggles.” Nicely said
46 minutes ago · Like
- Nico Rojas i understand now
34 minutes ago · Unlike · 1
Abdul Ansari plus, the areas of the two were never equal?February 5 at 1:40pm · Like
Arthur FrohlichThank you. When I say that the fractal gets infinitely close to the circle I mean that as you continue to contort the square’s perimeter to match that of the circle you eventually have an infinite number of squiggles that are infinitesimal in height, which gives you something that looks very much like a circle.
Abdul: The areas become extremely close although they will never actually equal. this is because you have to remember that those squiggles contain a small area. it’s similar to 2^(-x) in that it will never actually reach zero although it gets very close.
Also, you can’t remove the corners as squares because if you remove squares from a right angle you will definitely not get a curve. you would have to be removing rectangles of changing dimensions to get a curve.
Also, I should be doing a lab reportFebruary 5 at 10:31pm · Unlike · 1
Jerry Hill ah–in your explanation “approaches” would seem to be used in the context that the ~shape~ approaches that of a circle more and more closely: you weren’t saying that the length of the perimeter was changing… good point–i now take your meaning.
thanks for elaboratingFebruary 5 at 11:51pm · Like
Jerry Hill and good luck with the lab report!February 5 at 11:51pm · Like