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