How do i construct an arbitrary equilateral triangle with out knowing its scale?
for e.g. pick two points a and b. make $60$ degree acute angles at point $a$ and point $b$ and the two angles meet at point $c$. This looks like a complete layman solution for drawing an equilateral triangle with out knowing its scale. Can anyone suggest me alternative approaches for this problem?
The following is just your construction, with details made explicit. Let $A$ and $B$ be any two distinct points. Use a compass to draw the circle with centre $A$ that passes through $B$. Then draw the circle with centre $B$ that passes through $A$.
The two circles meet at points $C$ and $D$. Each of $\triangle ABC$ and $\triangle ABD$ is equilateral. For let $r$ be the radius of the circles. Then $AB=r$. But since $C$ is on each circle, we also have $AC=BC=r$.
Remark: This is Proposition 1, Book I of Euclid's Elements.