### trivia

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Hello all,

There have been some excellent comments by Moschops containing interesting pieces of trivia.

I have a couple too, maybe others can add theirs here as well.

The English stopped using Roman numerals some where around the 13th century. They adopted the Arabic numerals (1-9). Apparently it improved their book keeping abilities no end.

I am not sure, but the concept of zero may have invented even later.

Looking forward to more interesting stuff.
The equals sign was invented in 1557 by a Welsh mathematician called Robert Recorde:
 ...to auoide the tediouſe repetition of theſe woordes : is equalle to : I will ſette as I doe often in woorke vſe, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicauſe noe .2. thynges, can be moare equalle.

Translation into modern English:
 ...to avoid the tedious repetition of these words: "is equal to", I will set, as I do often in work use, a pair of parallels of one length, thus: =, because no two things can be more equal.
I have gained a load of trivia from watching QI.

Ancient greeks thought the sky was bronze, since they had no word for blue.

There's also the origin of x, the unknown variable used through out mathmatics, I don't remember the exact story but it was some kind of translation problems, the arabics named it something then the spanish translated it, and the way they said it made it sound like 'x', which spread to other countries, there's a TED talk about it, let me see if I can drudge it up.

https://www.ted.com/talks/terry_moore_why_is_x_the_unknown.html
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Thanks for your input guys - Good Work!!

Haven't heard from Moschops yet !! No doubt he is busy helping people.
Zero came from India, it's said to come from a Hindu concept of nothingness, but I don't really know about it.

There are, however, lots of links to all sorts of references in Google.
http://www.calculatoredge.com/math/mathhistory/historyans4.htm
QI is an awesome show for random trivia. Very little of it is purely mathematics, and not all of it is always interesting, but the large majority is very enjoyable and often scientific-in-nature trivia.
The ancients Greeks were switched on dudes - they were aware of visual perspective. The Parthenon is apparently 200 metres long and half way along the floor is 75mm higher than the ends. This solves the perspective problem so now it always looks flat and not distorted by perspective.

The columns have a radius of about 1 mile, so they don't look as if they are getting narrower as they go up. To build this radius, they drew a column 1 foot high on paper, drew a radius on this that they could physically draw. Then they divided the column up to represent cylinders (almost) sitting on top of each other. They measured the radius for each cylinder as it was on paper. When the cylindrical blocks were constructed, they had the same radius as on the paper, but were stretched in length, so a cylinder that was 1 inch high on the paper was say 3 feet high in real life - pretty clever really.
Did you know that the US Mile is about 1/3 of an inch (approx. 8mm) longer than the English mile?

Prior to SI conversion, an inch was 25.400126mm. The SI conversion is 25.4mm exactly, so multiplied by 63360 inches in a mile this makes the difference. The English of all people made a hard change and used the new 25.4mm conversion. The US however continued to use the old conversion, so their unit is still the same.

I am a Land Surveyor, and we have to take things like this into consideration. On trig station plans prior to 1968, we use the old conversion, because distances of 10miles say makes a difference of 80mm, which is important to us. These days we use GPS it's much easier.
 half way along the floor is 75mm higher than the ends
What? What does that mean?

What??

Biggest damn columns, ever!
 The ancients Greeks were switched on dudes

It amazes me how advanced the Ancient Greek's were in mathematics. About 2000 years ago, they had the most impressive library in Ancient History, the Library of Alexandria. The library also had a large museum, and zoo. It also had housing for researchers who lived there in the library with their families while they did their research. Archimedes, and Euclid are a few famous mathematicians who studied there.

Euclid proved that there is an infinite amount of prime numbers. The proof is like this:

Make a list if prime numbers , : 2, 3, 5, 7 ... P(n). Let P be the product of the terms p(1) thought P(n), plus 1.
`P = (2 * 3 * 5 * ... * P(n)) + 1 `

If the sum is prime, then you have a prime number greater than any primes in the list.

If P is not prime then, like all integers, it must have a unique prime factorization; and so it must be divisible by a prime number.

But it cannot be any primes in the list because
`P mod (any of the primes in that list ) = 1`.

So there exists some prime not in your list.
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 half way along the floor is 75mm higher than the ends

this means the middle is higher than the ends. E.g If the ends of the floor (ie the corners) were 100.000 metres above sea level, then the middle of the floor would be 100.075 metres. So the floor is not flat.

 Biggest damn columns, ever!

When I said radius I meant in a vertical sense !! (-:D) I don't what the diameter of the columns was, but say it was 2 feet, the radius of 1 mile is from the top of the column to the bottom. I didn't elaborate on that part because clearly the columns are not 2 miles thick! Also the method the Greek's used gives clues, and the example was about vertical perspective.

Thanks for the replies - hopefully there's more interesting trivia out there.
 When I said radius I meant in a vertical sense !!
Why didn't you say "height", then? Why would you say "radius" to refer to the non-circular part of a cylinder?

 the radius of 1 mile is from the top of the column to the bottom
That's not a less absurd measurement. No building has ever reached the 1 km mark.
Hi helios,

Sorry to cause so much confusion. I will have another go at explaining it.

Say the columns have a diameter of 2 feet at the top and the bottom. Say the column has a height of 36 feet. The diameter halfway up the height of the column (18 ft higher than the bottom) might be 2ft 1/2inch - so just 1/2 inch more than at the top or bottom of the column. So we have 3 points the top, the middle, and the bottom. These 3 points define an arc which will have a large radius. I haven't worked exactly what the radius for this example, but I am saying that radius on the real thing is about 1 mile. So the column is not cylindrical - it's shape in section has convex sides. It is this shape that gives the illusion that there is no vertical perspective.

Just to make sure I have fully explained this time, perspective is the illusion of narrowing as the distance away from the observer increases. Like standing between rail tracks, they seem to narrow up as they head away towards a vanishing point. It can also be seen in a vertical sense, columns seem to get narrower the higher they are, especially when the observer is near to the base of the column. It is this illusion the Greeks were trying to avoid, so that's why they made the columns curved and not cylindrical.

Hope this is all clear now.
Shay' (thing) -> shay -> xay -> x

The zero is of Indian origin meant nothingness indeed. But the Arabs used the zero to fill empty locations/digits
Also, let's not forget the Egyptians who built the pyramids - some serious engineering there.
Many stories say that aliens helped building them :D
 Say the columns have a diameter of 2 feet at the top and the bottom. Say the column has a height of 36 feet. The diameter halfway up the height of the column (18 ft higher than the bottom) might be 2ft 1/2inch - so just 1/2 inch more than at the top or bottom of the column. So we have 3 points the top, the middle, and the bottom. These 3 points define an arc which will have a large radius. I haven't worked exactly what the radius for this example, but I am saying that radius on the real thing is about 1 mile. So the column is not cylindrical - it's shape in section has convex sides. It is this shape that gives the illusion that there is no vertical perspective.

That's still bogus. An arc spanning over 35feet with a depth of 1/2feet would still be less than 40feet of length. To get your 1mile arc length, the columns would have to be bigger than our biggest buildings.