# MEASUREMENTS

These are the measurements based on the side-elevation from reference 1. Each measurement was taken from this picture with a centimeter ruler. The origin is centrally located at the base of the base cone (at the left end of the line marked "c"). The height of each triangle layer was measured (located to the left of the cone), while the differences between each triangle layer were computed (located to the right of the cone). The vertex of the main cone was determined by connecting various points along the sides and center of the triangle layers.

This diagram displays the method of determining the radius of the base layer, r0. This method deviates from the method of calculating the radius at any given height explained in the main cone section because the main cone begins above this layer. The measurement of the window along the base is 5.17 cm. This is determined based on the side-elevation [reference 1] seen above. The method of finding r0 uses trigonometry instead of equations of proportions. Dropping dotted lines down to a circle in the plane establishes two points along the circle. The line connecting these points is part of the hexagon layer. Extending these dotted lines even further forms a right triangle with r0 as the hypotenuse and 5.17 cm as its base. The angle between r0 and the radius is 30o based on a diagram from the triangle layer section. Since

cos 30o = 5.17/r0
then
r0 = 5.17/cos 30o
so
r0 = 5.97.

 Optical Illusion & Projection in Domes: A Study of Guarino Guarini's Santissima Sindone