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Numbers

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Posital
1141822.  Fri Jul 17, 2015 1:32 pm Reply with quote

Wiki wrote:
123,4567.89 China
!!!

Strange folk...

 
Zziggy
1142166.  Tue Jul 21, 2015 3:07 am Reply with quote

Numbers is a book in the Torah/Bible in which God kills approximately 150,000 of his "chosen people" for grumbling and then condemns the rest to die in the wilderness when they refuse to invade Canaan.

 
WordLover
1142204.  Tue Jul 21, 2015 8:27 am Reply with quote

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Last edited by WordLover on Fri Sep 16, 2016 11:18 am; edited 1 time in total

 
Zziggy
1142208.  Tue Jul 21, 2015 8:47 am Reply with quote

I learned it was probably phi while writing my masters, but I'm aware there's not much evidence either way. As I said, the reason (some) people think it was phi was because this value is important to the pentagram, which was a symbol of the Pythagoreans.

E.g. source , source.

The other story is as you say that he discovered the irrationality of the square root of 2.

Either way, he is often credited with proving the existence of irrational numbers and the legend is that he was drowned at sea because of it.

It's about as close to fact as you can get with any story from ancient times, imo :P

 
Zziggy
1142245.  Tue Jul 21, 2015 11:24 am Reply with quote

Pi is probably the most famous transcendental number. You probably know that, being irrational, the decimal (or any base in fact) representation goes on forever, randomly. However, it has some very nice non-decimal representations:


In 1593 the French mathematician François Viète proved that


While one I learned the proof of in complex analysis is Euler's


A simple infinite sum that probably most mathematics students will learn is Leibniz's formula


But one from the fifteen century by Nilakantha converges even quicker:


(All images from Wikipedia)

 
Zziggy
1142248.  Tue Jul 21, 2015 11:36 am Reply with quote

If you know another transcendental number, I bet it is e. It is roughly 2.718281828459045... but like pi, it goes on forever randomly.

e is equal to


But if you don't like that you can work it out as


If you'd prefer continued fractions,


There is also Pippenger's product


Again, all images from Wikipedia.

I'd like to do more but I wouldn't know how to write them without somebody having already made them into pngs and putting them on Wikipedia, so if the elves are interested I thoroughly recommend the book The Pleasures of Pi, e and Other Interesting Numbers by Y. E. O. Adrian. It's full of these sorts of thing.

 
Zziggy
1142249.  Tue Jul 21, 2015 11:38 am Reply with quote

So, having covered pi and e, we have the curious fact that



e^pi is called Gelfond's constant; nobody knows why it is nearly identical to pi+20 other than a crazy coincidence.

 
PDR
1142259.  Tue Jul 21, 2015 12:29 pm Reply with quote

Zziggy wrote:

I'd like to do more but I wouldn't know how to write them without somebody having already made them into pngs and putting them on Wikipedia


If you have MS Office you can create the equations in powerpoint (using the equation editor) and then save them as PNGs when you're done. These would be text on a white background (by default - you can change it).

There is a trick to giving the PNGs a transparent background, but I've forgotten what it is.

HTH,

PDR

PS - is my memory making it up, or do I remember that some of the most accurate pre-20th century estimates of Pi were calculated by imprisoned french aristocrats (passing time awaiting the guillotine) who spent time dropping needles on parallel lines a few thousand times or something? My memory is suggesting that estimates accuret to 6 or 7 significant figures were achieved, but it's quite possible I made it up.

 
Zziggy
1142261.  Tue Jul 21, 2015 12:39 pm Reply with quote

You can estimate pi that way, it's true! It is mentioned in one of the Maths-based 500 word essays, which is to my slight shame where I first heard about it.

However, those aristocrats wouldn't have been the most accurate even if they did pass time that way; Chinese mathematicians calculated pi accurate to about 7 decimal places by the 5th century, and Jamshīd al-Kāshī got to 17 decimal places by the early 15th century.

 
Zziggy
1142262.  Tue Jul 21, 2015 12:41 pm Reply with quote

PDR wrote:
If you have MS Office you can create the equations in powerpoint (using the equation editor) and then save them as PNGs when you're done. These would be text on a white background (by default - you can change it).

Thanks. I imagine I would have to upload it to an image-sharing website as well? There isn't a way of uploading an image to the forum directly?

 
PDR
1142272.  Tue Jul 21, 2015 1:46 pm Reply with quote

No, this forum doesn't do image-hosting (presumably to save server space and cost).

But a basic photobucket account is free and pretty easy to use - you upload a file, view it in your library and just control-V the "direct" URL and paste it between a pair of {img} tags (but with square brackets, obviously) in your post.

HTH,

PDR

 
suze
1142293.  Tue Jul 21, 2015 5:02 pm Reply with quote

Photobucket is all very well, but I like it less than I used to because the way that it currently works means that anyone who has the link to one of your saved pictures can fairly easily see all the others. Which may not be what you want.

When I want to post an image to these forums or to any of the other forums that I read, I'm currently using a service called http://postimage.org/. It's free and you don't have to register, create an account, or anything of the kind.

While this is unlikely to be relevant to images to be posted to these forums, this service even allows adult material provided that you identify it as such when you upload it. Most of the well known image hosting sites don't.

Other similar services are available, and I'm not particularly endorsing that one, just saying that it's easy, free, and it works.

 
14-11-2014
1144621.  Sat Aug 08, 2015 11:12 am Reply with quote

Quote:
A simple infinite sum that probably most mathematics students will learn is Leibniz's formula

Number skills, maths skills...

According to a dyscalculia test (20 out of 20, 1:40 including aiming and scrolling) your number skills may be excellent, but such a result doesn't mean that your mathematical skills are excellent. You won't have to understand nor use more complicated formulas while taking such a free internet test.

If almost all formulas look like secret code to you, then perhaps a score of 19 out of 20 would have been better. If you don't understand formulas, then your skills aren't as perfect as 20 out of 20, but it still isn´t a problem.

skillsyouneed.com wrote:
Improved numeracy skills lead to better paid jobs, greater well-being and a less stressful life.

Numeracy skills are not just for scientists, accountants and the tax man, many professions require at least a basic level of understanding when it comes to numeracy and mathematics. Take some time to develop your numeracy skills - it's never too late to learn.

Chris Humphries, Chairman of National Numeracy, talking to the BBC said:

“It is simply inexcusable for anyone to say ‘I can’t do maths.’”

He continued to suggest that many people cannot get jobs because they struggle to read graphs and interpret documents, while plumbers may find it difficult to do the necessary calculations to install a boiler and as a result lose income.

It may come as a surprise that almost half of the working-age population (17 million) of England have numeracy skills equivalent to those expected for an 11 year-old child.

This problem is not unique to England or the UK.

If you want to find out that you can do Humpries' maths, then testing (basic) numeracy skills will hardly scratch the surface.

 
WordLover
1144960.  Wed Aug 12, 2015 5:30 am Reply with quote

.....


Last edited by WordLover on Fri Sep 16, 2016 11:20 am; edited 1 time in total

 
WordLover
1145016.  Wed Aug 12, 2015 10:14 am Reply with quote

.....


Last edited by WordLover on Fri Sep 16, 2016 11:20 am; edited 1 time in total

 

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