Category Archives: Math

SPF = x^2 + 2x – 3

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Uncertain Principles: Algebra Is Like Sunscreen

My one-word piece of advice for students planning to study physics (or any other science, really, but mostly physics): Algebra.

Since we’re on the topic of math, let’s double the fun by visiting Cocktail PArty Physics: NEW VOICES: “math sucks”

“When I write, I can say whatever I want to say, but in math there’s just one right answer.”

She had a point there. I loved mathematics for its concreteness, its lack of ambiguity. It felt to me like a solid anchor in a hostile, subjective world. But the flip side of that is you can be definitely, unambiguously, totally wrong. You can’t plead “I was robbed,” like you can when the blind umpire calls you out or your sterling essay is marked with a D minus by a demented grader.

But … if the education is bland, and

[T]he core problem she faces, as she enters middle school “hating” math, is the math teaching itself, gender neutral, uninspiring for all.

There is the open question of why Austin (a boy) loves math.

I think an underlying issue is our desire to be able to point to a single problem to fix, when in reality there are multiple reasons why it’s tough to get kids to eat their vegetables learn their algebra.

Yes, We Think About Things Like This

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ArXiv: Minimizing the footprint of your laptop (on your bedside table)

We are considering all placements of the laptop such that it will not topple o the table;
these are exactly the placements for which the midpoint of the laptop is also a point of the
table. We are then interested in determining for which of these placements the footprint of the laptop is of minimal area; here, the footprint is the common region of the laptop and the table.

Healthy Graphing Technique

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An interesting graph of life expectancy vs per-capita income, for a bunch of different countries around the world. What is so trés cool is that you can animate it to run it from 1800 to the present. France does a meteoric rise very early on with no change in income, war participants take hits in life expectancy, and basically the whole world does the Time Warp (it’s just a jump to the left) in 1929.

Prime Surprise

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New Pattern Found in Prime Numbers

Since the late ‘70s, researchers have known that prime numbers themselves, when taken in very large data sets, are not distributed according to Benford’s law. Instead, the first digit distribution of primes seems to be approximately uniform. However, as Luque and Lacasa point out, smaller data sets (intervals) of primes exhibit a clear bias in first digit distribution. The researchers noticed another pattern: the larger the data set of primes they analyzed, the more closely the first digit distribution approached uniformity. In light of this, the researchers wondered if there existed any pattern underlying the trend toward uniformity as the prime interval increases to infinity

I linked to a video about Benford’s law a while back.

What About the Other Half?

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Poll: How many millions are in a trillion?

I’m not sure which is worse: that only a fifth of the respondents knew the answer, or that two-thirds thought they knew, and were wrong.

This report presents the findings of a telephone survey conducted among a national probability sample of 1,001 adults comprising 501 men and 500 women 18 years of age and older, living in private households in the continental United States.

Gee, I'm a Tree!

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The Geometry of Bending

When you bend a thin strip of an elastic material you get a beautifully shaped curve. What geometry does this curve follow? Can the curve be calculated if you know the length of the material and the position of the end points? Is it possible to calculate more complex situations with several forces in different directions? Can you make similar calculations in 3d? Can this geometry be useful in design/production?

(Hint: when in doubt, guess “yes”)

That's Odd

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Thursday is an Odd Day

Odd Day is coming Thursday, 5/7/9. Three consecutive odd numbers make up the date only six times in a century. This day marks the half-way point in this parade of Odd Days which began with 1/3/5. The previous stretch of six dates like this started with 1/3/1905—13 months after the Wright Brothers’ flight.

Analyzing Dr. Seuss

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Physicists can geek anything up. Analyzing the sizes of the cats in The Cat in the Hat Comes Back

The Cat in the Hat comes back and gets small

Ok, so Cat A is a little different (I will assume that is close before – or close enough). Cat B, however, doesn’t fit the pattern I used before. So maybe each successive Cat is not just 0.37 times smaller than the previous. I could explore this further if only I had more data. I do! Here is the next picture from the book.

The conclusion:

Don’t trust the Cat in the Hat.