 Copyright 20112017. All Rights Reserved.
Twitter Updates
 RT @MathFeed: A Mathematician is Grateful For… mathwithbaddrawings.com/2017/11/15/am… (by @benorlin) 6 days ago
 RT @ZeroSlope: 5 Ways to Troll Your Neural Network mathwithbaddrawings.com/2017/10/18/5w… 1 month ago
 RT @benorlin: https://t.co/quDciWDmZj 1 month ago
 RT @benorlin: https://t.co/UxRSgaz0lR 2 months ago

Recent Posts
 My Letter to the Wall Street Journal
 Quarter the Cross: An Elegant Construction
 Quarter the Cross
 My FT Alphaville Commentary on Managing U.S. Treasury Debt
 NAMA in NOLA
 Taming Premium Bonds
 Fifth Annual Municipal Finance Conference
 Generating Sitemap Links with Excel
 Spaghetti Puzzle #1
 A Mathematician’s New Year’s Resolutions
Top Posts & Pages
 Fast Formulas #1: Average Life of Mortgage (as Scheduled)
 Fast Formulas #3: Pool Average Life with CPR Prepayments
 Puzzle #2: Weighted Average LTV
 Good Fences Make Good Spreadsheets, Part 1
 Fast Formulas #2: Average Life of Mortgage (Amortizing with Balloon)
 Fast Formulas #3: The Spreadsheet
 Financial Math Puzzles
 Puzzle #1: Mortgage Average Life
 Puzzle #2: Followup Questions
 Fast Formulas
Recent Comments
Win Smith on Puzzle #7: The Mysterious… Elijah DePalma on Puzzle #7: The Mysterious… Rod on Puzzle #2: Weighted Average… My Letter to the Wal… on The National Debt is Closer th… Bob Rosinsky on Quarter the Cross Win Smith on Fast Formulas #1: Average Life… Win Smith on Quarter the Cross Bob Rosinsky on Quarter the Cross Mohammed Mustafa on Fast Formulas #1: Average Life… Win Smith on Fast Formulas #2: Average Life… Categories
Archives
Tag Cloud
 Average Life Formula
 Benjamin T. Solomon
 Big Data
 Bond Math
 Bond Math Puzzle
 Bond Puzzle
 Brandeis University
 Brookings Institution
 Calculus
 Calendar Puzzle
 Callable Premium Bonds
 Carmen Reinhart
 Christmas Trees
 Closed Formula
 Conferences
 Cool Graphs
 Derivative
 Excel Tables
 Fast Formulas
 Federal Reserve
 Finance Math Puzzle
 Financial Math
 Floating Rate Debt
 FRNs
 GARP
 Geometric Series
 Gravitation
 Halton Sequence
 Humor
 Innovations
 Interest Rate Risk
 Japan
 Johann Sebastian Bach
 Ken Rogoff
 Loan Average Life
 Marc Faber
 Math
 MATLAB
 Matt Henderson
 MortgageBacked Securities
 Municipal Bonds
 Municipal Finance Conference
 Optimization
 Physics
 Pi Day
 Precious Metals
 Prime Numbers
 Public Debt
 Pure Math
 Puzzle
 Puzzle #1
 Puzzle #2
 Puzzle #3
 QuasiGeometric Series
 Quasirandom
 Quotes
 QWAFAFEW
 Representing Numbers
 Seeking Alpha
 Space Travel
 Spreadsheet Tips
 Talks
 TED Talks
 The Bond Buyer
 Thomas Herndon
 Treasury Debt
 Treasury Floaters
 Tsunami
 U.S. Treasury
 U.S. Treasury Debt
 UC Denver
 volunteerAKITA
 Weighted Average Life
 Weighted Average LTV
 Weighted Average Maturity
Blogroll
Consultants
Father/Daughter Math Adventures
LinkedIn
My Company
Recommended Music
Tumblr
Meta
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
Leave a comment
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