Tag Archives: Pure Math

Happy 5 2 0 1!

Posted on January 1, 2016 by Win Smith

Last year,  in Happy 0 0 1 0 0 1 0 0 0 0 1!, I discussed an interesting way to represent numbers based on their prime factorization.  For example, 63 is represented by 0 2 0 1 because 63 = 20 … Continue reading →

Posted in Math | Tagged , , | Leave a comment

Puzzle #11: The Answer (Pi-Fingered Aliens)

Posted on May 19, 2015 by Win Smith

I posted Puzzle #11 on Pi Day (3/14/15 in the U.S.).  I noted that the sequence of numbers in 3.14159… reflects not just π, but also ten, the base we use for our numbers. The question was: What is 30.12120111…? After no … Continue reading →

Posted in Puzzles | Tagged , , | Leave a comment

Puzzle #11: A Pi Day Problem

Posted on March 14, 2015 by Win Smith

I thought of this Pi Day puzzle yesterday* while getting a haircut. I was thinking about this video by Vi Hart: Many people think that π is special because of its infinite digits. Hart disagrees. Most numbers are irrational like π, … Continue reading →

Posted in Puzzles | Tagged , , | 3 Comments

Happy 0 0 1 0 0 1 0 0 0 0 1!

Posted on January 1, 2015 by Win Smith

Most systems for representing numbers are a combination of the visible and invisible. In the familiar base-ten system, we represent numbers by linking visible digits to an invisible scaffold of powers of ten. For example, 534.08 implies the respective multiplication … Continue reading →

Posted in Fast Formulas, Math, Music | Tagged , , , , | 3 Comments

A New(?) Way to Visualize Numbers

Posted on October 1, 2012 by Win Smith

After I saw Matt Henderson’s visual demonstration of how the geometric series 1/4 + 1/16 + 1/64 . . . adds to 1/3, I thought about how to generalize this for any geometric series. This led to a way to … Continue reading →

Posted in Fun, Graphic Presentation, Math, Visualization | Tagged , , , , , | Leave a comment

Derivative of the Quotient: Lost in Translation?

Posted on June 30, 2011 by Win Smith

I posted a while ago about an alternate way to calculate the derivative of a quotient. Suppose G and H are functions of one or more variables.  For F = G/H, the standard form of the first derivative is: F’ … Continue reading →

Posted in Math | Tagged , , , , , , | 3 Comments

Derivative of the Quotient

Posted on April 25, 2011 by Win Smith

Given a function F = G/H, the first derivative is usually expressed as (HG’ – H’G)/(H^2) But this is equivalent to: (G’ – F H’)/H The second form seems to be easier to implement in some cases and requires less … Continue reading →

Posted in Math | Tagged , , , | 2 Comments