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I was thinking about making $\sqrt 3$ by folding (for example $A4$ paper). I do $\sqrt 2$ as a simple folding like below :

Square root 2

Remark: It is easy to make $\sqrt2 , \sqrt5$ by folding by $1:1$ and $2:1$ ratio.
But I got stuck on making $\sqrt3$ somewhat similar to that way or making some easy folding, Or using Theodorus spiral in folding.

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    $\begingroup$ once you have made $\sqrt2$ by folding now fold the same paper while keeping the perpendicular side $1$ and you wil get $\sqrt 3$ $\endgroup$
    – Yash Shrivastava
    Commented May 7 at 6:39
  • $\begingroup$ I was looking for a way to get $a^2+b^2=3n$, but as $\forall a \in \mathbb{N}: a^2 \mod 3 = 1$, this means that $a^2+b^2$ will never be $3n$, so that's not an option. $\endgroup$
    – Dominique
    Commented May 7 at 6:53

1 Answer 1

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You can continue the same to get ${\sqrt{2}}^2+1^1={\sqrt{3}}^2$

square root

You have the Dotted line at $\sqrt{2}$ , fold it to align that length along the Base. The Green line shows where the Point at the top will map to the Point at the Bottom. The Blue is always $1$.
Now the Purple line is $\sqrt{3}$.

Continue to the next Green line getting folded where the next Blue line is forming a triangle. The next Purple line is $\sqrt{4}$

Continuing , the next Purple line is $\sqrt{5}$

Continuing , we can get ${\sqrt{n}}^2+1^1={\sqrt{n+1}}^2$

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