Figure 4. Dihedral Angle α Referring to Fig. 4, since b and c both have endpoints on circle C, Δabc is an isosceles triangle with dihedral angle between the two equal sides. If we construct a great circle arc from point SC to midpoint D of side a, we will bisect Δabc into two congruent right […]
Figure 3. Isosceles Spherical Triangle ∆abc Point SC is the intersection of the z-axis with sphere S such that ∠SNSOCO = = ∠SNSOSC. There is a spherical triangle ∆abc that, when solved, will express the relationship between , , , and such that: Side a is great circle arc of length Side b is great […]
Figure 2. Coordinate System In the model as illustrated in Fig. 2, small circle C has a circumference that is 45º of latitude. We will be using the conventional terminology where a circle on the surface of a sphere that is made by the intersection of the sphere with a plane passing through the sphere center […]
Figure 3.1 Mathematica Model The animation in Fig. 3.1 above is an illustration of a mathematical model that was produced by Hans Milton in Mathematica. The model captures two smooth functions that are interdependent in normal, orthogonal, Euclidean 3-space. The illustration shows an animation of the visual components of this relationship. Also in the animation are […]
Figure 2.1 – NIST Subway Diagram So, what is direction, really? Currently, direction is an orphan when it comes to understanding physical quantities and how they relate to one another. The basic unit that is used to define an angle, the radian, is the disconnected unit at the lower right in the NIST diagram. […]
Figure 1.1 The Map of Physics – Image by Dominic Walliman Direction (or orientation) is a component of space. No one seems to disagree with this arrangement. There doesn’t seem to be any authoritative source on whether direction is a property, quality, quantity, attribute, parameter, constant, or whatever. Some experts claim that it’s a thing that […]
