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Dan Eastwood
"Information itself has a liberal bias." - Steven Colbert, 28NOV2006
"Information itself has a liberal bias." - Steven Colbert, 28NOV2006

Dan's posts

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Decoherence makes a lot of sense.

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Beware the new normal.

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Tony wildflowers

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Is it just me, or does anyone else think the Wonder Woman theme music sounds strangely familiar?

I won't say what it reminds me of yet, I don't want to influence responses/

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Jean Sammet 1928/03/23 – 2017/05/20

Mathematician and Computer Scientist Jean Sammet who reached the top of her profession despite the resistance of the educational system to the progress of smart women, has died at the age of eighty-nine. Amongst other accomplishments she was part of a small team that provided an initial design for the business-oriented computer programming language COBOL.

The programming language Ms. Sammet helped bring to life is now more than a half-century old, but billions of lines of COBOL code still run on the mainframe computers that underpin the work of corporations and government agencies around the world.

More here (obit.):

Jean E. Sammet was born on March 23, 1928 in New York City. Jean and her sister Helen were born to Harry and Ruth Sammet who were both lawyers. Jean and Helen attended public elementary schools in Manhattan. Sammet had a strong interest in mathematics but was unable to attend the Bronx High School of Science because it did not accept girls. Instead, Sammet attended Julia Richman High School.

Sammet chose to enroll at Mount Holyoke College based on the strength of its mathematics program. Sammet majored in mathematics and took education courses, which allowed her to be certified to teach high school mathematics in New York. She minored in political science. After graduating from Mount Holyoke, Sammet pursued graduate studies at the University of Illinois, where she received her MA in 1949. While taking courses toward a Ph.D., she was a teaching assistant in the Mathematics department at the University of Illinois from 1948 to 1951.

In 1951 Sammet began looking for a position in education. Sammet was forced to search for positions in New Jersey because New York City was not hiring new teachers. The authorities in New Jersey determined that Sammet was missing two courses from her studies: a course in education and one in the history of New Jersey. Sammet fought this determination, stating that her knowledge of New Jersey history did not strengthen her ability to teach mathematics in high school. This forced Sammet to seek other types of employment.

More here (Wikip):

Image: Computer History Museum

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What's the angle on this?
The most annoying (elementary) geometry problem

Suppose you’re given a triangle ABC (for which you have been told the angles at A and B), and you draw a line from A to a point E on the opposite side, BC, and a line from B to a point F on the opposite side, AB, such that these lines lie at specified angles to the base of the triangle, AB.

What, then, is the angle AEF, which we call x?

It’s possible, of course, to solve for the general case by slogging through a fair bit of trigonometry and algebra, to obtain a formula for x in terms of the four inputs to the problem: the two angles needed to specify the shape of the triangle, and the two angles that the extra lines AE and BF make with AB.

But if we choose these four angles correctly, it actually becomes possible to solve the problem without any trigonometry, and just a tiny bit of algebra, using elementary facts about isosceles triangles.

One version of this problem is known as Langley's Adventitious Angles problem. I was rather hoping that this was because the CIA invented it as a slightly more humane form of torture than their usual methods, but actually it was devised by the British mathematician Edward Mann Langley in 1922.

What’s annoying about this? If you state the problem (with an appropriate choice of angles) and tell someone that it can be solved by elementary methods, without offering any further clues, they might spend a very long time trying to find the “easy” path to the solution.

If you want to know the solution, there’s a nice explanation in this video:

Full disclosure: after trying for two hours to solve the problem the “easy” way myself, I caved in and watched the video.

So if you want to infuriate people at dinner parties by innocently drawing a diagram with a few angles on it, and telling them it’s a problem that your 10-year-old child solved for their maths homework, here’s the recipe for making sure that the angles are such that it really can be solved by elementary methods:

Define the angle BAC to be α
Set the angle ABC to 120°–α/2
Set the angle BAE to 3α/4
Set the angle ABF to 90°–α/2

The original problem concerned an isosceles triangle ABC, so there the choices were:

Set the angle BAC to 80°
Set the angle ABC to 80°
Set the angle BAE to 60°
Set the angle ABF to 50°

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