Science, Math, Physics, Chemistry, etc.

Science, Math, Physics, Chemistry, etc.
Cleveland and the Great Lakes region

Michelson–Morley Experiment
Conducted in 1887 by physicist Albert A. Michelson of Case School of Applied Science and chemist Edward W. Morley of Western Reserve University.

Donut or Coffee Cup?
Geek Math

Great tweet from Vincent Pantaloni: If you're a topologist (Helvetica font style) there are 8 (capital) letters in the English alphabet.

Capital letters

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Flip a Coin
Geek Probability

The Great Lakes Geek often gets questions about gambling and the lottery. Just the other day I was asked to figure the odds of a tossed coin landing on 'heads' after 9 'heads' were tossed in a row.

I explained and the person still does not believe the answer. I told him that if a fair coin is tossed and heads comes up 9 times in a row it has no effect on the next toss. A coin has no memory so there is still the usual 50-50 chance of tails or heads. The previous 9 or 900 tosses have nothing to do with that next toss.

The confusion is about the probability of tossing 10 'heads' in a row. That's a whole 'nother smoke.

The probability of one head in a row is 1 out of 2 (.5), the probability of 2 heads in a row is 1 out of 4 (.5 x .5), 3 heads is 1 out of 8 (.5 x .5 x .5) and so on. So the probability of 10 heads in a row is 1 out of 1024 (.5 to the 10th power) or .0009765625.

In a real world case where someone tosses 9 heads in a row I would be concerned about the fairness of the coin.

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Lotto Math
Geek Math

The last post about the probability of tossing a coin and getting 10 heads in a row prompted a question about the lottery. The conversation between Leonard's mother Beverly and Sheldon on the Big Bang Theory comes to mind:

Beverly: Is that a rhetorical point, or would you like to do the math?

Sheldon Cooper: I'd like to do the math.

Beverly: I'd like that, too.

Here we go. Say there are 44 possible numbers and you have to pick the lucky 6 to win. How many ways are there of choosing a 6-number combo from the 44?

The formula is C (44,6) which is 44 factorial divided by (6 factorial x 38 factorial) or 44! / (6! *38!). Then the probability of coming up with a specific 6 number combination is 1 over that number.

Refresher: Factorial is the product of that number and all the positive integers less than it. So, 6 factorial, designated as 6! is the product of 6x5x4x3x2x1 or 720. Factorial get huge fast. For example, 10! is 3,628,800. So 44! is huge and 1/44! is minute.

To see the chances for a particular lucky number being in the selected 6, you want to find the probability that the winning 6 number combination will contain any given number. First, you want to figure out how to not pick that number.

You have to choose the 6 numbers from the other 43 so use the formula C(43, 6). There are C(44,6) - C(43,6) combinations which include your lucky number.

The probability is then that result divided by C(44,6).

Moral? Don't quit your job to win the lottery.

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Classic Topology Book
Geek Freebie

It's been a long time since the Great Lakes Geek studied topology and he wasn't around when they used this book. But it's great to see John Kelley's classic graduate level textbook from the 1950s-70s in general topology available online in a variety of formats for free.

General Topology book

Grab your own copy of General Topology by John Kelley

NASA Earthrise - 45th Anniversary
Geek Space

This video shows how the world's most famous photo actually got captured and how the 3 astronauts had to scramble to get color film in the camera and roll the module. Very cool.

Feynman Lectures on Physics
Geek Link

The famous Feynman Lectures on Physics is a physics textbook based on some lectures by Richard P. Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were given to undergraduate students at the California Institute of Technology (Caltech), during 1961-1963 and have been a favorite for aspiring physicists ever since.

The three volumes of the book focus on mechanics, radiation, and heat, including relativistic effects (Vol 1), electromagnetism and matter (Vol 2) and quantum mechanics (Vol 3).

In case you didn't know (or forgot) in 2013, Caltech in cooperation with The Feynman Lectures Website made the book freely available, on the web.

As the site says, "Now, anyone with internet access and a web browser can enjoy reading a high quality up-to-date copy of Feynman's legendary lectures. This edition has been designed for ease of reading on devices of any size or shape; text, figures and equations can all be zoomed without degradation.

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