Understanding of this representation of π can be summed up as:īut that might just be the fault of the representation. As far as I know, the state of our current This being the case, it is perhaps not too surprising that nobodyĬan make head or tail of the representation of π, which isģ.14159265358979. Not because it is a simple number, but because 31250 happens to divide Simpler representation than a simple number like 1/3 just demonstrates Representation of 1/3 is 0.33333., which isn't even finite. Like simple numbers to have simple representations. It should be fairly clear that, as a representation of real numbers,ĭecimal fractions are not very satisfactory. Is no more or less complicated than any other number. They know more mathematics than they do, who want to argue that π Really, this section is here to address people who think If you don't need to be persuaded that π is unusually weird, evenĪs transcendental numbers go, you may want to skip to the next In fact, the degree to which π is not understood is rather You often hear π mentioned in the same breath withĮ, another constant of fundamental mathematical importance.īut e is much more tractable than π is, and much better π is an extremely peculiar number, even by mathematical In this section, I'm going to argue that the question is indeed worthĪsking. Of Euclidean geometry, and why I think it is more complex than people Finally, I'll look at the essential properties Property of Euclidean geometry, one which does not occur, for example, This is important,īecause the relation between π and circles appears to be a special Then I'llĭiscuss Euclidean and non-Euclidean geometries. Weird if you do agree, feel free to skip this section. I expect that almost everyone will agree that π is Of Euclidean geometry: specifically, that its metric is a nonlinearįirst I'm going to spend some time arguing that π does requireĮxplanation. Very weird and complex number π with a geometric object as simpleĪs a circle is a reflection of the underlying fundamental complexity The one-paragraph summary: My theory is that the association of the I thought about this pretty hard, and, to my amazement, I came up with Simon Cozens wrote to me yesterday to ask what the heck was up withĬircle makes it. The Universe of Discourse : Why pi? The Universe of DiscourseĬompass points in Czech Math SE report 2023-10: Peano's definition of addition is not a tautology, and what was great about Ramanujan? Obsolete spellings and new ligatures in the names of famous persons Uncountable sets for seven-year-olds A Qmail example of dealing with unavoidable race conditions Puzzling historical artifact in “Programming Erlang”? Math SE report 2023-09: Sense and reference, Wason tasks, what is a sequence? Advice to a novice programmer Help wanted: blog redesign Cats in Romance languages Portuguese food words in Asia The discrete logarithm, shorter and simpler
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