Archive for the ‘Mathematics’ Category

Bizarro pi(e)

March 14, 2017

For Pi Day, 3/14, from Chris Hansen, this 2005 Bizarro:

Not only the pi connection, but also a Dan Piraro piece of pie.

horsetails

February 19, 2017

… the plant, viewable locally in planters outside two office buildings, one a block north and one a block west of where I live. They thrive there; they are tough plants, aggressive even — they are invasive pest plants in South Africa and Australia — though they suffer some from vandals who manage to break their stems off. The local species, Equisetum hyemale, in a big stand:

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More number fun

August 12, 2016

(No linguistics that I can see.)

A follow-up to my posting on Collatz sequences, picking up an open question in one-symbol Smullyan systems, from an obscure 1970 paper by Stephen Isard and me.

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Collatz days

August 11, 2016

Every so often, things coincide. In the last couple of days, Jeff Shaumeyer relayed on Facebook an 8/9 posting on Jason Kottke’s blog with a delightful video about the Collatz Conjecture, and then a day later I got a phone call from Greg Huber at UC Santa Barbara about this very same conjecture in number theory and its possible connection to a paper Steve Isard and I wrote 46 years ago (in previous lives) on “one-symbol Smullyan systems”. And there’s an xkcd:

(#710 from 3/5/10)

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Anti-spam architect (plus a mathemagician)

May 21, 2016

The anti-spam architect would be Elizabeth Zwicky in a “Yahoo Women in Technology Profile” by Michael McGovern (Talent Community Manager at Yahoo!) on the 18th. The piece is in the form of an interview, but with questions submitted in writing by McGovern and answers written out by EDZ, so you get the full flavor of her writing — lucid, pointed, often wry. There are photos: one of EDZ with her team, one an unposed head shot of her which catches her nicely. It’s a bit too light, a consequence of the fact that the photographer (Opal Eleanor Armstrong Zwicky, then age 6) was a novice at the camera, though she already had a good eye):

(#1)

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Graphic novel: Logicomix

April 24, 2016

One more comics-related posting for the day, but no gay connection this time:

Apostolos Doxiadis & Christos H. Papadimitridou (art by Alecos Papadatos, color by Annie Di Donna). Logicomix: An Epic Search for Truth (2009)

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xkcd on science and math

March 16, 2015

(Only marginally related to linguistics.)

Two xkcd cartoons from the world of science (the fundamental forces of physics) and math/computer science (NP-complete problems):

(#1)

(#2)

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The Pides of March

March 15, 2015

Yesterday was Pi Day — a particularly good one, 3/14/15 in American date format (for 3.1415) — and today is the Ides of March. So: the Pides of March.

Pi (that is, π) is a transcendental number (in a special mathematical sense of transcendental). Now, a few words about different kinds of numbers.

We start with the natural numbers, the ones we use for counting things: 1, 2, 3, 4, … Everything else is an extension from these: zero (0), fractions, negative numbers, imaginary (vs. real) numbers, complex numbers, irrational (vs. rational) numbers, transcendental (vs. algebraic) numbers, and more.

Most people deal with only a few of these types, and then usually in the context of calculating values for practical purposes, like calculating the area of a circle (A = πr2). For these purposes, we can restrict ourselves to non-negative real numbers, which will be dealt with in computations via decimal fractions.

The universe of these numbers:

1. rational numbers, expressible as the quotient p/q of two integers (q ≠ 0), with two subtypes as decimal fractions;

1a. terminating decimals, like .1 (for 1/10), .2 (for 1/5), and .5 (for 1/2);

1b. repeating decimals, like .142857142857142857… i.e. .142857, with an underline marking off the repeated part (for 1/7); for practical purposes in computations, approximations will be necessary (say, .14 for 1/7);

2. irrational numbers, not so expressible (so their decimal expansions will be non-terminating and non-repeating, and approximations will be necessary for practical purposes in computations), with two subtypes:

2a. algebraic irrationals; an algebraic number is the root of a polynomial equation with rational coefficients. For example, √2 ( = 1.414…), the positive root of x– 2 = 0.

2b. transcendental irrationals, ones that are not algebraic, like π ( = 3.1415…).

It took some considerable time for people to accept the existence of irrational numbers. Pythagoras balked at the idea. Now it turns out that most numbers are irrational, and indeed, nearly all numbers are transcendental. Most of us just don’t have to deal with many of them.

(Teachers often give approximations to irrationals for the purpose of computation; 22/7 or 3 1/7 is sometimes suggested as a approximation to π for these purposes, and then since 1/7 = .142857, you might want to approximate that, as 3.14 or 3.143.)

The creatures of Fibonacci

January 18, 2015

(About art and mathematics rather than language.)

In the January 16th San Francisco Globe, the article “3D Printed Sculptures Look Alive When Spun Under A Strobe Light”:

This series of 3D printed sculptures was designed in such a way that the appendages match Fibonacci’s Sequence, a mathematical sequence that manifests naturally in objects like sunflowers and pinecones. When the sculptures are spun at just the right frequency under a strobe light, a rather magical effect occurs: the sculptures seem to be animated or alive! The rotation speed is set to match with the strobe flashes such that every time the sculpture rotates 137.5º, there is one corresponding flash from the strobe light.
These masterful illusions are the result of a marriage between art and mathematics… the [Fibonacci] sequence starts with two 1’s, and each following digit is determined by adding together the previous two. Therefore, Fibonacci’s Sequence begins: {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…} etc.
… The creator of these sculptures, John Edmark, is an inventor, designer and artist who teaches design at Stanford University

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Sconic sections

July 10, 2013

From several sources on the net, this entertaining story posted 6/25/13 on the Evil Mad Scientist site:

Play with your food: How to Make Sconic Sections

The conic sections are the four classic geometric curves that can occur at the intersection between a cone and a plane: the circle, ellipse, parabola, and hyperbola.

The scone is a classic single-serving quick bread that is often served with breakfast or tea.

And, at the intersection of the two, we present something entirely new, delightfully educational, and remarkably tasty: Sconic Sections.

Detailed instructions follow. The edges of the sections can be highlighted by jam, chocolate, or Nutella (as above).

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