So x and y axioms have an angular relationship and the z axioms phi is independent, having half the values because its the same on either side of the axis without concern with position. Hmm interesting stuff.
Changing the frame of reference from what I described here is a bit more advanced than what I can cover here, but I would assume we need all 3 axes to define a frame of reference.
thank you SO MUCH for this video. It got me unstuck. I didn't realize that the vertical angle goes only from 0 to Pi, not to 2Pi, like angles usually would
Great animation.Thanks. You have my subscription. I think greatly of all the pre computer graphics mathematicians who could see it all in their heads.Makes one wonder? In the long run are our brains going to be less or more capable of visualisation?
That's such an interesting question. I feel like we are adding to the number of people that can visualize a topic each time we express it in a new way. There's no shortage of difficult concepts to understand, so I suppose anyone can still exercise the skill as much as they want. I had a colleague suggest that some boys gain an advantage in spatial visualization over girls from jumping off of playground equipment and tracking movements of the ball in sports more often. I have no idea if nature or nurture is the main culprit, but I suspect it's a skill that can be strengthened.
Hi Everyone. I'm realizing I didn't rescale my screen capture, so a lot of this video is covered up. I'll record and upload an updated version tonight.
θ is to reduce the aggregate of three-dimensional space to a surface, Φ is to reduce the aggregate of a surface to a line, which is the intersection of the surface and the cone, and ρ is to reduce a line to a point. The positioning of any point in space can be completed.
This was very concise! Illustrated fantastici! All important key features in order to calculate the transmitted irradience by angular dependent. Using Yours - presented coordinates and the following spherical coordinate system I can specify a given direction for the zenith and azimuth angles thus the transmittance of this system is a function of direction of incident radiation. So valuable information also for the irradience from the sun, sky and for all hemispheric areas given by the independent of changes in the sun or sky radiance. Thank you because performing an integration of the transmitted irradience and calculating the total radiant flux in civil engineering we can see better geometry for example water, glass, polarized elements, i. c. Also we can imply two-dimensional Fourier transform of Cartesian coordinates if we understand better first important step that implys in all disciplines not only engineering approach! 👏👏👏👏
I am attempting to make a truncated dodecahedron skeleton out of wood for a hobby carpentry project. At what angle do the decahedrons meet? At what angle do the triangles meet? Thank you in advanced. I keep looking for answers online but I just keep encountering math way beyond my level.
Hello! I made these again in blender and got the following results: A dodecahedron is made up of pentagons, the angle between each of the two pentagons is 64.635 degrees. When you truncate it, you should get triangles and pentagons. The angle between every triangle and decagon (10-sided) should be 37.377 degrees. Let me know how the project turns out, or better yet, send pictures!
