February 2012
8 posts
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Pi
Here are some rational approximations to pi that I computed, each entry looks like: {fraction, decimal expansion of that fraction (to 15 digits), percent error}. Just a reminder- pi to 15 digits is 3.14159265358979.
{4, 4.00000000000000, 27.3}
{3, 3.00000000000000, 4.51}
{19/6, 3.16666666666667, 0.798}
{160/51, 3.13725490196078, 0.138}
{1744/555, 3.14234234234234, 0.0239}
{644/205,...
January 2012
5 posts
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty cold...”
– BERTRAND RUSSELL, Study of Mathematics
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December 2011
3 posts
5 tags
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November 2011
16 posts
4 tags
Project Euler
I just solved the most recent project Euler problem (I’m number 189 !) and I thought I might share my solution. The problem was:
An infinite number of people (numbered 1, 2, 3, etc.) are lined up to get a room at Hilbert’s newest infinite hotel. The hotel contains an infinite number of floors (numbered 1, 2, 3, etc.), and each floor contains an infinite number of rooms...
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Generating Functions and Fibonacci
I was looking at some of the Project Euler problems the other day and I found some pretty neat solutions using generating functions and Mathematica. For example:
“By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.”
My solution in Mathematica was:
Normal[Series[2/(1 - 4 x - x^2), {x, 0, 10}]] /. x ->...
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Books About Math
I am putting a list of math books here (the list is from The Art and Craft of Problem Solving by Paul Zeitz) in hopes that I will be more motivated to read them.
Books about Algebra:
Polynomials by E.J. Barbeau
The Cauchy-Schwartz Master Class : An Introduction to the Art of Mathematical Inequalities by J. Michael Steele
Books about Combinatorics:
An Introduction to Combinatorics by Alan...
October 2011
1 post
5 tags
Mandelbrot Set
As you can probably tell by the little picture at the top there, I really like Mandelbrot Sets. Consequently I have been trying to write a program to draw some of my own. Unfortunately Mathematica is kind of slow when it comes to number crunching, so I tried to write something in python. With a little help from the pylab examples, I was able to come up with the following.
import numpy as np...