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## Re: [ontolog-forum] Beauty in mathematics -- detected in brain scans

 To: ontolog-forum@xxxxxxxxxxxxxxxx John F Sowa Fri, 21 Feb 2014 09:54:07 -0500 <5307688F.4090305@xxxxxxxxxxx>
 ```On 2/20/2014 7:57 PM, Rich Cooper wrote: > Found a Wikipedia page on it: > > http://en.wikipedia.org/wiki/Euler%27s_identity    (01) That's one of the best Wikipedia pages I've seen: it explains Euler's identity in a concise way that both a novice mathematician and anybody who teaches (or has taught) math could enjoy.    (02) The graphic animation on the upper right side of the page illustrates the beauty of the abstract math. It shows the result of repeated multiplications for computing (1 + iπ/N)^N as N goes to infinity.    (03) But a bit more explanation might make it clearer:    (04) N=1. The value of (1 + iπ/1)^1 is the endpoint of a line that starts at (1, 0) and goes straight up to (1, 3.14159).    (05) N=2. The value of (1 + iπ/2)^2 is (1 + iπ/2)*(1 + iπ/2). That is represented by the endpoint of a bent line that goes from (1, 0) to (1, 1.57) and then to (-1.467, 3.14).    (06) N=3. The value of (1 + iπ/3)^3 is represented by the endpoint of a bent line with three segments.    (07) As N goes to infinity, the graph converges to a semicircle that goes from (1, 0) to (-1, 0).    (08) John    (09) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (010) ```
 Current Thread [ontolog-forum] Beauty in mathematics -- detected in brain scans, John F Sowa Re: [ontolog-forum] Beauty in mathematics -- detected in brain scans, Rich Cooper Re: [ontolog-forum] Beauty in mathematics -- detected in brain scans, Rich Cooper Re: [ontolog-forum] Beauty in mathematics -- detected in brain scans, John F Sowa <=