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Tag Archives: Pure Math
Happy 5 2 0 1!
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
Puzzle #11: The Answer (PiFingered Aliens)
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
Puzzle #11: A Pi Day Problem
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
Happy 0 0 1 0 0 1 0 0 0 0 1!
Most systems for representing numbers are a combination of the visible and invisible. In the familiar baseten 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 Fundamental Theorem of Arithmetic, Prime Numbers, Pure Math, Representing Numbers, WellTempered
3 Comments
A New(?) Way to Visualize Numbers
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 Georg Cantor, Matt Henderson, Pi, Pure Math, Representing Numbers, Visualizing Numbers
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Derivative of the Quotient: Lost in Translation?
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 Calculus, Cool Graphs, Critical Points, Derivative, Mathematica, Pure Math, Russian Translation
3 Comments
Derivative of the Quotient
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