Timeline for Transcendental numbers as infinite products of sides of squares
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2013 at 15:46 | vote | accept | Vassilis Parassidis | ||
| Oct 1, 2013 at 5:35 | answer | added | Robert Israel | timeline score: 2 | |
| Oct 1, 2013 at 5:19 | review | Close votes | |||
| Oct 1, 2013 at 20:47 | |||||
| Oct 1, 2013 at 4:45 | comment | added | Vassilis Parassidis | @AaronMeyerowitz.The first product converges to 2/pi. This product is well known, the Vieta product. The second product converges to the square root of e. | |
| Oct 1, 2013 at 4:32 | comment | added | Aaron Meyerowitz | If you pick $x_0$ and then iterate $x_{n+1}=\sqrt\frac{1+x_n}{2}$ then the limit, if any, should be a number $L$ such that $L=\sqrt\frac{1+L}{2}.$ Solve that for $L$, find that neither solution is transcendental and observe that the limit does exist. | |
| Oct 1, 2013 at 4:24 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
added 1 characters in body
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| Oct 1, 2013 at 4:14 | history | asked | Vassilis Parassidis | CC BY-SA 3.0 |