Out of all of my 2024 videos so far, all of the ones that are about intersections have dislikes because someone's butthurt that I don't include roundabouts. I don't dislike roundabouts, I just prefer traffic light intersections because they are more convenient. I dislike that people are so obsessed with them that they think they should be everywhere just because they are "safer". I'm going to do another video about intersections next month. But if it gets 2 dislikes like the others, then that just proves my point.
These are the 5 most basic regular shapes: (Top is 2D - Bottom is 3D)
#1 This is the polygon with the most simple math. Both the angle between edges and faces are 90 degrees.
#2 This is the polygon that has the fewest number of sides, while still having an area. The angle between edges in 2D is 60 degrees, and between faces in 3D is arcos(1/3). (~70.528779)
#3 This is the polygon where the distance from the center to each corner is the same length as each side. The angle between edges in 2D is 120 degrees, and between faces in 3D is arcos(-sqrt(1/3)). (~125.26439)
#4 This is the lowest limit of sides. This is technically a 1D shape, but as 2D, the angle between edges is 0 degrees.
#5 This is the highest limit of sides, and the only shape where all directions are exactly the same distance from the center. If scaled up where the length of sides are larger than 0, the angle between edges in both 2D and 3D, is 180 degrees.
Which nelinda member would have the low range of a contrabass clarinet, and the high range of a baritone saxophone?
Here are 5 of the most useful equiangular polygons:
The 1st one is a square.
The 2nd one is a square that has half of the sides lengthened by a factor of 2, to have a side length ratio of 2:1. Any factor other than 1 makes a rectangle. lengthening the side to infinity makes what I call a circumscribed digon, though impossible to see. Making them 0 instead makes a digon that has no area.
The 3rd one is a regular hexagon.
The 4th one is a regular hexagon that has half of the sides lengthened by a factor of 3/2, to have a side length ratio of 2:1.
lengthening the same sides by a factor of 3 makes the 5th one, which is an equilateral triangle. Any factor other than 0, 1, and 3 makes a truncated triangle, though more than 3 makes a negative truncated triangle instead.