Category Archives: Math

September in Paris

In a previous post, I described a paper on sovereign debt by Mattia Landoni (Cox School of Business – Southern Methodist University), Christopher Cameron (US Treasury), and me.  Our paper gives a simple way to relate debt management policies and … Continue reading

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Bond Talk on May 23

‏If you’re in Denver on May 23 and you’re interested in the bond market, join us for a QWAFAFEW* talk: Predicting the Supply of Long-Term Bonds.  The talk will be based on a new paper by Mattia Landoni, Chris Cameron, … Continue reading

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New Paper on Bond Portfolio Dynamics

  Mattia Landoni (SMU Cox School of Business) and I recently completed a paper on bond portfolio dynamics (now under review at an academic journal). We offer a new theory on the evolution of the maturity structures for rolling bond … Continue reading

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Quarter the Cross: An Elegant Construction

Last month, I presented an infinite pattern of nested crosses as a response to the  #QuarterTheCross challenge on Twitter.  The idea is to find interesting ways to shade one-quarter of the area of the cross built from five squares.Now David Butler, a math lecturer … Continue reading

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Quarter the Cross

Yesterday, I noticed that some of the math teachers I follow on Twitter were challenging their students, and themselves, with the #quarterthecross problem.  The problem is simply to find interesting regions of a five-square cross that take up exactly one-quarter of … Continue reading

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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

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Fast Formulas #6: Finding the Time

  The Fast Formulas on this blog provide shortcut calculations for financial instruments such as mortgages and bonds. Most formulas involve the symbol n to represent the number of periods (e.g. years or months) until the end of the instrument. Usually … Continue reading

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A Mathematical Family Tree

I am delighted by what I just learned about my mathematical family tree.  It started with this tweet by scientist and writer Paul Halpern: More than 120,000 mathematicians can trace their scholarly heritage back to Byzantine thinker Manuel Bryennios: reading

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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 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

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Puzzle #9 (Follow-up): Melting Fractals

The song “Let it Go” from the movie Frozen celebrates “frozen fractals.” I suppose a frozen fractal is something like the Koch snowflake. Lately, though, one of my puzzles has made me more interested in melting fractals. The challenge of Puzzle … Continue reading

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