Dan MacKinnon

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mathematical lapses

Dan MacKinnon posted an article on - Nov 27, 2009, 8:52 pm
Every man has somewhere in the back of his head the wreck of a thing which he calls his education. - Stephen Leacock, A Manual of Education I recently stumbled upon some of Stephen Leacock'...
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interesting and uninteresting numbers

Dan MacKinnon posted an article on - Nov 19, 2009, 8:56 am
In a paper published this week on arXiv, Dann van Berkel mentions the famous proof (or joke, depending on how you view things) that all natural numbers are interesting. Essentially, if there are unint...
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symmetry on TED

Dan MacKinnon posted an article on - Nov 9, 2009, 12:45 pm
To see any pure math lecture on TED is exciting. Why are these things so rare? A recent talk by Marcus du Sautoy, Symmetry, reality's riddle, is now availalbe here. Marcus du Sautoy is a prol...
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The Calculus of Friendship - a review

Dan MacKinnon posted an article on - Nov 3, 2009, 12:17 pm
In The Calculus of Friendship, Steven Strogatz, a Professor of Mathematics at Cornell, gives us a memoir of the friendship he has maintained with his former high school teacher, Don Joffray, as reveal...
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another origami ideal

Dan MacKinnon posted an article on - Oct 30, 2009, 10:48 am
... that neither artistic expression nor technical complexity are important to my own experience of origami. Perhaps that is because I lack both artistic and technical talent. I was encouraged, howe...
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JUMP math

Dan MacKinnon posted an article on - Oct 29, 2009, 10:23 am
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Harmonic Denominator Number Triangle

Dan MacKinnon posted an article on - Oct 27, 2009, 11:55 am
This number triangle is made up of the denominators of the Leibniz Harmonic Triangle. From the earlier post about that number triangle, you can see that there are two ways of generating the Harmonic D...
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Mesopotamian maths

Dan MacKinnon posted an article on - Oct 23, 2009, 11:18 am
On Notation. Whether one believes that mathematics is created or discovered, notation is certainly created. And notation can direct the course of mathematics.  - Elisha Peterson,...
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whither blogger LaTeX?

Dan MacKinnon posted an article on - Oct 19, 2009, 8:28 am
If you have a Blogger blog, you may be using some $\LaTeX$ renderer to make your math look nice. A couple of days ago, the one I was using (from www.watchmath.com) stopped working (hopefully it w...
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Math Teachers at Play 17

Dan MacKinnon posted an article on - Oct 15, 2009, 10:24 am
... Pumpkin Patch: Piggy Bank Math Game posted at Pumpkin Patch. Much has been written on math blogs lately about how to understand and explain "negative multiplied by a negative is positive...
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Three number triangles, two telescoping series

Dan MacKinnon posted an article on - Oct 7, 2009, 9:22 pm
There are so many relations present that when someone finds a new identity, there aren't many people who get excited about it anymore, except the discoverer! - Donald E. Knuth (as quoted by M...
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beautiful negatives

Dan MacKinnon posted an article on - Oct 5, 2009, 9:48 am
teacher (emphatically): A double negative makes a positive, but a double positive can never make a negative! student (lazily, from the back of class): yeah, yeah... I am not sure where this top...
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math teachers at play

Dan MacKinnon posted an article on - Oct 3, 2009, 9:20 am
Math Teachers at Play blog carnival, edition 16, is up at I want to teach forever. The next MT@P blog carnival will be hosted here at mathrecreation in two weeks on Oct 16, 2009. Please send...
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Is zero a triangular number?

Dan MacKinnon posted an article on - Sep 29, 2009, 9:23 pm
Neil Sloan's On-Line Encyclopedia of Integer Sequences, which every one who works seriously (or recreationally) with integer sequences regards as the ultimate authority, lists the triangular numbe...
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means and trigonometric ratios

Dan MacKinnon posted an article on - Sep 27, 2009, 8:02 pm
I recently noticed that two earlier posts contain an identical diagram (surprising how these things slip by). Both instances of the diagram come from old high school textbooks, one dedicated to geomet...
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envelope of the Wallace line

Dan MacKinnon posted an article on - Sep 23, 2009, 9:43 pm
I was looking at  Heinrich Dorrie's 100 Great Problems of Elementary Mathematics, and problem 53, which involves a surprising hypocycloid construction, caught my attention. The problem i...
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a bit more origami

Dan MacKinnon posted an article on - Sep 23, 2009, 9:44 am
This is just a footnote to an earlier post on origami. There is a really nice TED talk by Robert Lang where he explains why we like to use mathematics to solve problems (like, how to make paper bugs ...
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Rosencrantz, Guildensten & the gambler's fallacy

Dan MacKinnon posted an article on - Sep 15, 2009, 8:48 am
The opening of Tom Stoppard's play has Rosencrantz and Guildenstern  flipping coins and noticing that the 'laws of probability' seem to be suspended (you should check out the ope...
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geometric programming and trig functions

Dan MacKinnon posted an article on - Sep 10, 2009, 8:48 pm
... geometry programs is to consider 'sketching' as programming (an unhelpful way to think of sketching is to think of it as drawing). This orientation is explained ... R. Nicholas Jackiw ...
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a neglected sequence

Dan MacKinnon posted an article on - Sep 9, 2009, 10:32 am
Looking at some old texts (from the 1930s, mostly) I came across a type of sequence that was once part of the standard curriculum along side the familiar arithmetic and geometric varieties.  As f...
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scrambler fractal

Dan MacKinnon posted an article on - Sep 1, 2009, 8:02 pm
The image at the top of the post shows the first five generations of the family of curves obtained from the 'scrambler' construction that I described briefly in the last post. These curves are...
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hypocycloid scrambler

Dan MacKinnon posted an article on - Aug 28, 2009, 9:28 pm
The scrambler amusement park ride gives a visceral sense for how circular motions can be added together to create a trajectory that scarecely resembles a circle itself. If you watch (or get on) the ri...
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origami

Dan MacKinnon posted an article on - Aug 19, 2009, 12:11 pm
Exploring the mathematics of origami has been a pursuit of recreational mathematicians, educators, and mathematical researchers for some time. Martin Gardner's chapter on the mathematics of origam...
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triangulo-triangular numbers

Dan MacKinnon posted an article on - Aug 7, 2009, 2:29 pm
I recently learned from Janet Beery's paper, Formulating Figurate Numbers, that mathematicians have been referring to the 4-dimensional triangular numbers as the 'triangulo-triangular' num...
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~ 95 mathematicians

Dan MacKinnon posted an article on - Aug 5, 2009, 10:09 am
The BBC4 documentary Dangerous Knowledge (on youtube and on watchmath), although worth watching, promotes the popular but unfortunate notion that mathematicians are prone to madness. Timothy Gowers re...
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self referential

Dan MacKinnon posted an article on - Jul 23, 2009, 11:18 pm

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Euler on arXiv

Dan MacKinnon posted an article on - Jul 21, 2009, 11:16 am

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Annotated Math Blogroll 1

Dan MacKinnon posted an article on - Jul 15, 2009, 10:21 am

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Rhombic Hexecontahedron

Dan MacKinnon posted an article on - Jul 7, 2009, 12:18 pm

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mere calculation

Dan MacKinnon posted an article on - Jun 19, 2009, 9:39 pm

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