"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
-G.H. Hardy

"I know numbers are beautiful. If they aren't beautiful, nothing is."
- Paul Erdős

Dec
15
awarded Caucus
Nov
28
answered Working algorithm for testing two rectangles for overlapping in Earth GPS coordinates plain
Nov
25
revised Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
edited body
Nov
25
revised Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
added 43 characters in body
Nov
19
comment Box2d bodies that are really close together, are getting “stuck”
Great answer, thanks!
Oct
4
comment Is there a problem for which it is known that the only solution is "iterative"?
Sorry for the confusion. I have been studying numerical methods, where the problem is to construct a sequence of intervals which converges on the solution of an equation such as $x=cos(x)$. I consider the limit of this sequence to be "the solution". It's possible to write down such a sequence for $\sqrt{2}$ in a "closed form", whereas apparently the solution of $x=cos(x)$ has "no closed form solution". The problem of defining closed form solution was raised here, and motivates my question.
Oct
4
comment Is there a problem for which it is known that the only solution is "iterative"?
When you say no iterative method is neccessary, do you mean a method other than the Bisection method as described here?
Oct
4
comment Is there a problem for which it is known that the only solution is "iterative"?
To clarify what is meant to be "a solution", consider as an example the problem "Compute the solution to the equation $y=cos(y)$ that is accurate to 6 decimal places of it's actual value $x$", then clearly the word "solution" has it's normal meaning, namely: $x$ solves the equation. Suppose you wanted to increase the accuracy of this computation, could you do so without invoking an "iterative" process that depends on knowing the previous values of the sequence?
Oct
4
comment Is there a problem for which it is known that the only solution is "iterative"?
Me too! My question is specifically: is it possible to prove the statement "the only way to get it is by iteration" rigorously?
Oct
4
asked Is there a problem for which it is known that the only solution is "iterative"?
Sep
30
awarded Explainer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
1 2 3 4 5