Recent content by davidmoore63@y

It might be easier to plot the curve in polar coordinates, which are: r=n theta=Pi/2 - 2Pi/n

I don't like your proof! If you have x^n = 1 + x+ x^2 +...+x^(n-1) using the formula for the sum of a GP you get x^n = (1-x^n)/(1-x), and so x - 2 + 1/x^n =0 now you can see that as n tends to infinity x gets as close as you like to 2.

Similarly: Let S = 1+2+4+8+16+... 2S= 2+4+8+16+32+... So 2S= S-1 S =-1

One of the reasons people get confused is that they think the economics of government are similar to the economics of individuals. Hence, they think that if the US has a large amount of debt it's something to be worried about, as you would if you had a large personal debt. The crucial...

The squared length of a complex vector v is defined by v.v(bar) where v(bar) is the complex conjugate, i believe. That will give you sqrt2

(2,0) and (-2,0) do not satisfy the inequality

The equations of General Relativity do allow for space and time to reverse roles. For example, in the spherically symmetric Schwarzschild solution, time and space reverse roles sufficiently close to the center of mass (inside the event horizon of a black hole). Distance becomes the...

I did a math degree at an English university then had a career in trading in Wall Street. Lots of math there, mostly probability and statistics. In addition with the advent of conputerized trading, there's a need fur programmers. i did not decide about my career choice until the third...

The hands versus the rope: think Newton's third law. For the second question, consider that the tension along a rope must the the same (assuming the pulleys are frictionless), otherwise it would move

why don't you try approximating with a normal distribution

In fact I would expand on my previous post. When I started this book, aged 14 in 1977, I knew no calculus. I read it non stop for about a week, and completed all the exercises, by which time I was very comfortable with single variable calculus. What I particularly remember is how the book...

First calculus book I ever read (back in the 1970s), and the best introduction I have ever seen.

I find it helpful to think about conservative fields here. A force field grad T is a conservative field because it is derived from a scalar potential T. Now any circulatory path through a conservative field results in no change in potential, since it starts and ends at the same point. Hence...

Not much wrong with your work. I do have a quibble with your derivation. When writing A'(j,k)= C(j.m)C(k,n)A(m,n) you should use different dummy variables to prevent confusion with the dummy variables in the expression for Z. Thus A'(j,k)= C(j.p)C(k,q)A(p,q) is better. Then you can collapse...

appears to be a rational approximation to the correct answer < -1/sqrt 6, 2/sqrt6, -1/sqrt6 >