![]() ![]() Here is the stuff you can place in for the sphere equation: There you must use the variable x instead of time t. This post is seven pictures long (all of the usual size 550 x 775).Īll graphs in this post are made with the applets as found on:įor the two graphs from above look for ‘animated drawing’ choose the 2D explicit curves option. Only it is in 4D space and not in the two dimensional complex plane… You can numerically check this by adding the squares of the sine and cosine for all t in one period and that is all we do in this post. In the complex plane the sphere-cone equation is given by x^2 + y^1 = 1 (that is the unit circle) and if you read this you probably know that f(t) = e^ = cos t + i sin t. ![]() ![]() If you want to compare this post to the same stuff in the complex plane: So this post does not contain numerical evidence that the determinant is always one on the entire exponential curve. In 4D space the sphere-cone equations are not enough, there is at least one missing equation and those missing equations can be found in the determinant of a matrix representation M(Z) for a 4D complex number Z.īut we haven’t done any determinant stuff yet (because you also need a factorization of the 4D determinant in four variables and that is not a trivial task). In this post we will check numerically that the 4D exponential curve has it’s values on the 4D unit sphere intersected with a 4D cone that includes all coordinate axes. In 3D space the sphere-cone equations ensure the solution is 1 dimensional like a curve should be. This is Part 9 in the basics to the complex 4D numbers. ![]()
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