Geometric Definition and 811 Threads

Question: A man puts $10 in the bank for his son on each of his birthdays from the first to the twentieth inclusive. If the money accumlates at 3% compound interest, what is the toatl value on the son's twenty-first birthday? My answer is like this: a = 10, r = 1.03, n = 20 Total value = a...

Has anyone ever tried to make prime numbers into some kind of geometric equivalence? Such that prime numbers can be predicted through geometry? I was thinking of a universe beginning with one 3D unit, and evolving from that unit. That all subsequent units would have a relation to the first...

Hi, I have a relatively simple question. In this particular problem in my Math 30 Pure textbook... 10. Here are three levels in a school telephoning tree. Teacher Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 a)At what level are 64 students contacted? ...I really...

I understand that an example of a physical interpretation of the line integral of a scalar function with respect to arc length \int_C f(x,y,z)ds might be the total mass of a wire where f describes the linear density of the wire. But can anybody give an example of a physical or geometric...

Consider 3D geometric algebra. Let all points on a line be given by the parametrization x=tu+y, in which the parameter runs from minus infinity to plus infinity. a. Show that for all points on the line we have x(wedge)u=y(wedge)u. b. Show that the vector d pointing from the...

can anyone explain how commutators act on tri-vectors (in orthonormal conditions)? on bi-vectors i know that it ends up to be a bivector again, but with tri-vectors it vanishes if its lineraly dependent. what about the case if its not linearly dependent, does that mean it remains a...

Just wondering... so the conception is that gravity is not really a "force" but rather the consequence of shortest-path motion through curved geometry. Are there analogues for the other forces? I know gravity is not yet theoretically unified with the other forces. But is there nonetheless some...

I'm having trouble with these type of probles (where a negative log comes up): (All of this is solving without sigma notation) Find the number of terms in these geometric sequences and the sum of the numbers. 11, -22, 44,...,704 I know that a1 = 11, r = -2, and an = 704, so I did...

I'm trying to get an A in honors AlgII/Trig and it is impossible, but I won't give up, so I have a few questions. I'm not sure how to find the first two terms of a sequence (I got a few right, but most wrong and I don't know what's wrong). One of the problems is: a5 = 20; a8 = 4/25. I set...

Can you solve analytically [oo] [pi] (n)1/n n=1 or [oo] [pi] (n!)1/n! n=1 or [oo] [sum] (1/n)n n=1 or [oo] [sum] (1/n!)n! n=1 ?

Given n+1 points in n-dimensional Euclidean space, how many polytopes (generalizations of polygons of n to as few as 2 dimensions) may be defined by the representation of each point as a possible vertex?