The fascination of Maths thread

[beaker]

I did maths tutoring when I was 23. One of pupils was a very nice 16 year old girl. I only lasted 2 weeks...

... and?

[Denny]

I hated Maths, was useless at it and failed my O level. Algebra was the only thing I enjoyed, mainly because it had letters in. God knows how I got put into the O level group when there was a perfectly good CSE option available. I suppose I must have got too many sums right. Forget anything that involved compasses and triangles and rulers or those stupid questions you get in IQ tests.

What more can I say!

[BrowneIssue]

However what really really freaks me is that I would love to count in tpd!

I would do so, but it is against the rules...

[Diver]

Does your house address start with a 1? According to a strange mathematical law, about 1/3 of house numbers have 1 as their first digit. The same holds true for many other areas that have almost nothing in common: the Dow Jones index history, size of files stored on a PC, the length of the world’s rivers, the numbers in newspapers’ front page headlines, and many more.

The law is called Benford’s law after its (second) founder, Frank Benford, who discovered it in 1935 as a physicist at General Electric. The law tells how often each number (from 1 to 9) appears as the first significant digit in a very diverse range of data sets.

Blatantly Plagiarized coz I'm too lazy to write it myself

[NotAllThere]

I hated Maths, was useless at it and failed my O level. Algebra was the only thing I enjoyed...

I think rather that you hated calculation. If you liked algebra, you might have found A level and university maths much more interesting - there's very little real maths at O level.

According to a strange mathematical law, about 1/3 of house numbers have 1 as their first digit.

It's not just house numbers, it's also accounts that have this distribution of digits - mainly the last. This has been successfully used to spot fraudulent accounting. It's part of standard auditing now - get all the numbers and see the proportion that end in 0,1,2, etc.

[threaded]

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigor should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

threaded in "wrangler" mode

[VectraMan]

Does your house address start with a 1? According to a strange mathematical law, about 1/3 of house numbers have 1 as their first digit.

No, begins with a 9.

And surely that's more to do with the length of roads rather than any strange matematical law.

[TimberWolf]

I thought I'd start this as we seem to have hijacked another thread.
Strange and counterintuitive ideas in Maths to be posted here.
My favourite is the fact that the it takes just 23 random people for the odds of two sharing the same birthday to be 0.5. And if you have just 40 people those odds rise to 0.9.

And is sometimes called the birthday paradox/theorem/attack and is relevant to biometrics (and cryptography) in that a biometric that works okay to authenticate someone in a small group can quickly suck at identifying people in a larger group. Clearly anyone can be paired with anyone else in more ways (n^2-n)/2 than someone specific can be paired with anyone else (n-1).

And 367 people are needed to guarantee two people share the same birthday (includes leap years).

Exponential functions are also sometimes non-intuitive. For example folding a piece of paper doubles its width, so after 50 folds (impossible in practise) you have a piece of paper perhaps as thick as the distance to the moon (2^50 times its original thickness)

The Monte Hall problem is also a good puzzle.

[sasguru]

threaded in "wrangler" mode

Walter Mitty strikes again. What year were you a wrangler, Threaded?

[threaded]

Does your house address start with a 1? According to a strange mathematical law, about 1/3 of house numbers have 1 as their first digit.

Not strange at all, is called Benfords Law. Applies to any situation where the data is not quite random, and at the same time, not quite constrained.

When one has enough mathematical knowledge (and maybe a hint*) it is quite obvious why it happens in a head slapping way.

Actually doesn't have much to do with the lengths of roads. If you made all roads twice as long or doubled all house numbers, most house numbers would still start with a 1.

*Hint: consider this: if it happens then it would happen no matter what measurement scheme, i.e. if it happens with lengths in meters, then it should still happen if you measure in feet, or inches, or cubits. This shouts that some function involving exponentials is involved, and we all know repeated application of something like that either goes to infinity or 1.