(sqrt(w+x)²-R)²+(sqrt(y²+z²)-R)² = S²
There's a few different definitions for "torus" as a category of objects. I think the best one is "an object who's RNS notation has brackets around it". This includes tiger, but not torinder. The tiger is also a "beast", but thanks to RNS notation, beasts aren't as scary as they used to be.Actually, you're not correct. Sorry. A torus and a tiger are unrelated. There are several types of torii in 4D, but the tiger isn't one of them.
The 'tiger' is a tri-circular torus. It is the torus-product of three circles: its surface corresponds to the identification of the six opposite faces of a cube, in the same manner that the regular 3d torus does a square.
Icon wrote:i still dont get it.
I wrote:I know not everyone will understand this, but it's worth doing it anyway.
PWrong wrote:There's a few different definitions for "torus" as a category of objects. I think the best one is "an object who's RNS notation has brackets around it". This includes tiger, but not torinder. The tiger is also a "beast", but thanks to RNS notation, beasts aren't as scary as they used to be.Actually, you're not correct. Sorry. A torus and a tiger are unrelated. There are several types of torii in 4D, but the tiger isn't one of them.
PWrong wrote:The tiger is the torus product of a duocylinder and a circle: (2x2)#2.
Pwrong wrote:Try to understand all the other 4D shapes first. The tiger is the most difficult 4D rotope to visualise. Start with the tetracube, then spherinder, cubinder, glome and duocylinder in that order. You can find descriptions of these on the wiki or on alkaline's main site. Those are the rotatopes. Then have a go at the other rotopes: torinder, 3-torus, toracubinder, toraspherinder, again in that order. Only then will you be ready to battle the tiger!
did you guys make all this up? not saying its fake just that you came up with it all. the math for it too? and the language? soo all of these shape concepts aren't readily accepted by the scientific community? or are they?
The tiger and the 3-torus are not the same. The cartesian and parametric equations are different. I will believe that they're topologically equivalent when someone proves it. But it's obvious from the equations that they're not the same object.
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