Search found 13 matches

Fri Apr 08, 2011 11:36 am UTC
Forum: Mathematics
Topic: How do they calculate Pi?
Replies: 7
Views: 2834

Re: How do they calculate Pi?

Computing \pi in, say, 1000 digits, can be done very quickly using this equation: \pi=48 \arctan \frac{1}{18}+32 \arctan \frac{1}{57}-20 \arctan \frac{1}{239} where each of these three arctan values is approximated by \arctan x = x - \frac{x^3}{3} + \frac{x^5}{5}-\frac{x^7}{7}+\cdots I did it some t...
Mon Mar 14, 2011 12:18 pm UTC
Forum: Mathematics
Topic: The Mathematics of Perspective
Replies: 35
Views: 6099

Re: The Mathematics of Perspective

Am I missing something? ... The calculations don’t get any more difficult than arctan if I’m thinking it through correctly. The calculation of the perspective image of a point, based on both the Cartesian coordinates of that point and the spherical coordinates of the viewpoint, is very well known (...
Mon Mar 14, 2011 8:37 am UTC
Forum: Mathematics
Topic: The Mathematics of Perspective
Replies: 35
Views: 6099

Re: The Mathematics of Perspective

Instead of parallel projection as shown in my previous post, we can use a horizon with vanishing points, as shown below, to obtain a real perspective image. The cube edges AB and AD are constructed in the same way as with parallel projection. The vanishing points U and V are found as points of inter...
Thu Mar 10, 2011 1:54 pm UTC
Forum: Mathematics
Topic: The Mathematics of Perspective
Replies: 35
Views: 6099

Re: The Mathematics of Perspective

Here is a construction for parallel projection. We start with the vertical cube edge AE. The rotated square A'B'C'D', with sides equal to AE, provides vertical lines for the cube edges BF, DH and CG. The side A'B' of the rotated square can have any slope. Draw AB arbitrarily, but with a slope that i...
Wed Mar 09, 2011 7:43 pm UTC
Forum: Mathematics
Topic: The Mathematics of Perspective
Replies: 35
Views: 6099

Re: The Mathematics of Perspective

Basically, while drawing I have to guess how long to make the faces of cubes along the z-axis. This doesn't sit well with me, especially since I have had several works killed after realizing just how wrong I got the proportions. So, is there some kind of mathematical formula for calculating this? A...
Sat Feb 12, 2011 8:35 am UTC
Forum: Mathematics
Topic: Math Software
Replies: 143
Views: 163893

Re: Math Software

I get "syntax error at start" whenever I try to use the exp() function as part of the input. Thank you. There was an error in my code (due to confusion of x in exp with the variable x), which is now fixed. For example, with the given intervals for x and y, you can now enter exp(0.05 * x *...
Fri Feb 11, 2011 12:17 pm UTC
Forum: Mathematics
Topic: Math Software
Replies: 143
Views: 163893

Re: Math Software

Would this be any good for visualizing a function [imath]z = f(x, y)[/imath]?
http://home.kpn.nl/ammeraal/function/func3.html
Note that the user can easily change the viewpoint.
Since I wrote this myself, I would appreciate any comments that may lead to improvements.
Tue Jan 04, 2011 4:20 pm UTC
Forum: Mathematics
Topic: Bike trig: distance b/w sprockets connected by a chain
Replies: 2
Views: 1026

Re: Bike trig: distance b/w sprockets connected by a chain

Just for fun, I wrote an iterative program to compute the distance between the two axles, with given radius of each wheel and the length of the chain (or belt). I wrote this in C++. Can you handle the source code of this? If so, I can publish it here. If not, please let me know so I can help you.
Mon Jan 03, 2011 6:40 pm UTC
Forum: Mathematics
Replies: 6
Views: 1804

You wrote ... I got this question: "If your home consumes electrucity at the rate of one killowatt per hour..." I cannot imagine that you really got that question. Not only does it contain two spelling errors, but 'kilowatt per hour' is nonsense. You should not confuse units of power (kilo...
Sat Jan 01, 2011 4:21 pm UTC
Forum: Mathematics
Topic: Probability Query
Replies: 10
Views: 1476

Re: Probability Query

It is essential that the host knows what is behind each door. He deliberately takes a door that shows a goat. The probability for the door that you initially chose remains 1/3, and the probabilities for the two other doors together remains 2/3. Now that one of these two other doors turns out to have...
Sat Jan 01, 2011 3:01 pm UTC
Forum: Mathematics
Topic: A few questions about the golden ratio
Replies: 14
Views: 3779

Re: A few questions about the golden ratio

Suppose a line segment is divided into a smaller part of lengh 1 and a larger part of length \phi , in such a way that the whole line segment (of length 1+\phi ) is \phi times larger than the larger part: 1 :\phi = \phi : (1+ \phi) Then \phi = (1+\sqrt 5)/2= 2 \cos (\pi/5)=1....
Wed Dec 29, 2010 3:46 pm UTC
Forum: Mathematics
Topic: Help with spherical coordinates
Replies: 2
Views: 2268

Re: Help with spherical coordinates

sphcoor.jpg In this figure, you see that z_E = \rho \cos \phi and that the length of line segment z_E E is equal to \rho \sin \phi . Looking in the xOy-plane at the bottom you find the projection of this line segment, which has the same length. Multiplying this by \cos \theta , you find x_E = \rho ...
Wed Dec 29, 2010 10:09 am UTC
Forum: Science
Topic: Walking on an escalator
Replies: 15
Views: 15454

Re: Walking on an escalator

I agree with Zamfir, but I would like to clarify his last two sentences. At first I had the impression that he was completely wrong in writing here about work being equal to weight times velocity, and wanted to replace this with 'weight times increased height'. Then I realized that the vertical comp...