- Hence the equation or graph y=sinx is transformed into itself by
- T: x'=x+180°, y' =-y; likewise by the rotation through angle 180° about 0°, viz.,
- S: x'=-x, y'=-y.
- The product R=ST gives the reflection on the 90° vertical:
- R: x'=180°-x, y'=y.
- The infinite group transforming y=sinx into itself is generated by T and S.
- Let the cartesian coordinates of a point P of the rectangle be x, y, the x-axis being AB, the y-axis a perpendicular to AB at its center O. On the fan let the polar coordinates (origin O) of P be r, A. Then r =y, while the complement of A is measured by an arc of length x on the semi-circle.
- Compare Veblen's proof, Monthly, January, 1904, p. 7.
The American Mathematical Monthly
Volume 12, 1905 - Issue 6-7