  In this paper, we calculate period matrices of algebraic curves defined by
$$w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2)\cdots (z^2-a_{g-1}^2)$$ for any $g\geq 2$
and $a_1, a_2, \dots, a_{g-1}\in \mathbb{R}$ with $1<a_1<a_2<\cdots <a_{g-1}$.
We construct these algebraic curves from Euclidean polygons. A symplectic basis
of these curves are given from the polygons.
