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How do I square $\\log_2(3)$. Does it become $2\\log_2(3)$ ?
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Thus it now seems that a 3-dimensional structure whose base is a square with side $200$, whose top is a circle of diameter $100$, and whose height is $150$, cannot be constructed by bending and creasing a flat 2-dimensional shape.
$\begingroup$ First, $4+1+1=6$, so you can reach the residue class $6\pmod 8$. More importantly, yes, this is a result where (as it turns out) one has to deal with the powers of $4$ separately first, before finishing it off with the $7\pmod 8$ observation.
Saying this question is too localized makes no sense. Completing the square is an important tool. The OP doesn't know how to do it and is asking for help. That's a perfectly legitimate question. Saying it is too localized is completely wrong, as other people also may not know how to complete the square and could learn from the answers below ...
Suppose $(n,p) = 1$ and $n$ is a square mod $p$, so the square root in ${\mathbb Q}_p$ should exist. One quick way to explicitly find good approximations of it is ...
Two dissections of a square are equal if there is an isometric mapping of the square into itself, which maps the first dissection into the second one, but in this case no dissected squares can be equal.
One of the squares thus becomes non-covered. What are the possible positions where the empty square can be? If this is the relevant object to consider, and it should be arranged only horizontally, being an odd number, it cannot fill any row in the 8x8 grid, without leaving 2 squares unfilled.
which describes the parametric path of square shape, with the angle as parameter. For using it in a program following works also very well: Define $\varphi(x) = \max(0, \min(1, 3/2 - \vert x \vert))$ .
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