The fascination of Maths thread

[Denny]

Why do so many continent names begin with the letter A?

E.g. Africa, America, Antarctica, Asia, Australia.

And why do so many continent names end with the letter A?

Europe

Perhaps you should be asking why so many continents start and end with the same letter.

[Sockpuppet]

Nothing to do with that. This'll bake your noodle: it applies equally well to any position of the digits in the numbers. So how does that tally with your length of road conception?

Well yes it does.

Because I could say that the vast majority of roads in the UK have less than 200 houses on them. A fair assumption.

Therefore Numbers 1 - 10, 100 - 199 have number 1 at the beginning. Over half.

So if you found that a lot of streets either had <30 houses or have >100 but <200 houses on them then 1 would indeed be the number that a 1/3 of houses start with.

Its not mathematical super genius or a law its just the way towns have gorwn up with streets of X size etc.

[bored]

Well yes it does.

Because I could say that the vast majority of roads in the UK have less than 200 houses on them. A fair assumption.

Therefore Numbers 1 - 10, 100 - 199 have number 1 at the beginning. Over half.

So if you found that a lot of streets either had <30 houses or have >100 but <200 houses on them then 1 would indeed be the number that a 1/3 of houses start with.

Its not mathematical super genius or a law its just the way towns have gorwn up with streets of X size etc.

You are correct. The law works because if you take a generic number not tied to a specific scale, it is more likely to fall into the ranges between 10-19, 100-199, etc rather than 90-99, 900-999, ...

See http://mathworld.wolfram.com/BenfordsLaw.html

[BrilloPad]

We have all been to those meetings where someone wants over 100%.
Here's to achieving 103%.

Here's a little math that might prove helpful in the future!
What makes life 100% ??


IF,

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Then,

H A R D W O R K

8 1 18 4 23 15 18 11 = 98 % Only



K N O W L E D G E

11 14 15 23 12 5 4 7 5 = 96 % Only



But,

A T T I T U D E

1 20 20 9 20 21 4 5 = 100 %



However,

B U L L S H I T

2 21 12 12 19 8 9 20 = 103%

[OwlHoot]

Well yes it does.

Because I could say that the vast majority of roads in the UK have less than 200 houses on them. A fair assumption.

Therefore Numbers 1 - 10, 100 - 199 have number 1 at the beginning. Over half.

I'm sure that accounts for it in many situations, but in general Benford's Law relates more to logs. In the days before calculators it was he, or someone, who noticed that log tables were more tatty and worn in the ranges with low first digits, because the log function log(1 + 1/x) is decreasing for increasing x > 0 (and this fall off is more pronounced for small values of x, say 1 to 10).

Also, in my experience a similar thing tends to occur with the alphabet. If you sort a large number of typical surnames or book titles in English (ignoring starting prepositions such as "A" and "The"), you tend to end up with more than expected in the A-E range.

[TimberWolf]

We need a poll…with 366 choices

Here's a simple one.

When your age is your father’s birth year, he will be the age of your birth year.

So for example if your father was born 1950 and you were born 1980 then when you are 50, he will be 80.

This also works for your mother, brother or a pot of jam, but you'll have to deal with century boundaries or be optimistic about life expectancy and include the century so that when you are 1950 years old he will be 1980 years old.

[MrRobin]

Hey just discovered this thread. you lot were obviously unoccupied over the weekend...

I love the birthday paradox. Everyone gets confused by it One of my fav maths conundrums is the Game Show problem where there are 3 doors, behind one is a prize and on choosing a door, the host opens one of the other doors that he knows doesn't have a prize then offers you the chance to change your mind... do you?

Good maths book I only read recently was Fermat's Last Theorem, may have to check out Maor.

Brillopad, bet you're glad it wasn't a Desmond or a Douglas tho. Good lottery advice.

Series expansion always caused me trouble at school, still does.

Benford's Law makes logical sense but is interesting to know it has practical uses in fraud detection and cryptography!

Err... that's it.

[KathyWoolfe]

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

Why was this discovery called after Benford and not SImon Newcomb who discovered it in 1881, 57 years before Benford?

[crack_ho]

Hey just discovered this thread. you lot were obviously unoccupied over the weekend...

I love the birthday paradox. Everyone gets confused by it One of my fav maths conundrums is the Game Show problem where there are 3 doors, behind one is a prize and on choosing a door, the host opens one of the other doors that he knows doesn't have a prize then offers you the chance to change your mind... do you?

That pardox changed my life. When I heard it in my 'Risk' class I immediately left and took to injecting Heroin. I dont care about conditional probability, I will stick to my first answer 'cos I am always right. Anyway the prize would probably have been a speedboat and I have never seen the sea.

[Churchill]

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.

I think the numbers 3,4 and 5 are absolutely fantastic!

Churchill - In "Pythagorean triple" mode...