Super Pi moment * Four mysterious numbers and the most beautiful equation *

Strangely enough, the Pi symbol was first used by a Welsh mathematician called William Jones in his book Synopsis Palmariorum Matheseos in 1706. I thought it would be older than that.

K

-1

Negative numbers: The concept of negative numbers first appeared in China during the Han Dynasty between 200 BC and 200 AD. Their adoption through the rest of the world was slow. The Greek mathematician Diophantus, in the 3rd century, referred to an equation with a negative solution as absurd. Indian mathematicians in the 7th century were the first to widely use negative numbers and strangely they used the + sigh to denote them.

In the west people continued to be suspicious of negative numbers right up to the 18th century.

In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". He came to the conclusion that negative numbers were nonsensical.

In the 18th century it was common practice to ignore any negative results derived from equations, on the assumption that they were meaningless.

Gottfried Wilhelm Leibniz was the first mathematician to systematically employ negative numbers as part of a coherent mathematical system, the infinitesimal calculus. Calculus made negative numbers necessary and their dismissal as "absurd numbers" quickly faded.
[link to en.wikipedia.org]

K

bump for lovers of numbers. and numerals, their visual representations.

i

i the imaginary number. The square root of -1:

The concept of imaginary numbers may date back as early as the Greek mathematician Heron of Alexandria. Like the concept of -1 ( and 0 ) they were treated with suspicion and even derision by mathematicians such as René Descartes. It was Euler and Gauss who popularised their use in the eighteenth century.

Imaginary numbers can't be represented on the real number line but instead, a complex number, with real and imaginary parts, can be represented by a point on a complex number plane. [link to www.geom.uiuc.edu]

Multiplication by the imaginary number has the unexpected ( well maybe for me ) result of a 90 degree counter clockwise rotation of the point on the complex plane. This is something that will become important later.

K

The use of i is pretty much essential is all sorts of electronic and electrical engineering, anything to do with oscillating signals, AC power, phase angles, radio, Fourier analysis / signal processing, electrical impedance, reactance etc. Electrical engineers us j instead of i to avoid confusion with the symbol for current.

K

In the UK it will be the 31st April though!

Thirty days hath September...

K

E = pi r squared
but not really, because pie r round...

You want to know the truth?
Check this out:

Thread: Hacker Exposes 'Alien Deception' -The Real X-Files

Follow the link to the rikijo blog.

e

e, the base of the natural logarithm:

e was discovered by Jacob Bernoulli while he was investigating problems of compound interest. Bernoulli asked himself, if an account paid 100% interest in a year, what effect would paying the interest in monthly or daily increments have? Working through the problem with smaller and smaller increments he saw the end of year total approaching the value of e. e is another irrational and transcendental number, like pi. e can be found as the limit of the expression (1 + 1/n)^n as n -> infinity

[link to www.wolframalpha.com]

Here it is in its truncated glory.

2.7182818284590452353602874713526624977572470936999595..

e is also called Euler's number after the brilliant Swiss mathematician.

K

Which brings me to what has been called the most beautiful equation of all, Eulers identity.

e^i.pi = -1

[link to www.wolframalpha.com]

Who would have though on first glance that combining two irrational numbers and the imaginary number would have such a seemingly simple result.

You can also, of course, express it as

e^i.pi + 1 = 0

Thanks for the bumps Mr NorM and Beeches and everyone else. I have to go now but I will will check back later to seeif anyone wants to know the surprisingly simple reason why e to the i pi equals minus one.

K

Only day in 100 years we'll get that time too. Not sure what kind of pie I'll have to celebrate.

Anyway, remembering where I am is pi just a poser for tau?

the lore of numbers and numerals is fascinating. I wish it were taught in schools at any grade level.

math is not dry, unless you believe life is dry.

I thought it was Sesame Street

Wired calls it, "The Baffling and Beautiful Wormhole Between Branches of Math"

[link to www.wired.com]

Its conclusion, "Those crop-circle aliens were trying to tell us something."

K

Here is a proof using Maclaurin series for e^x, cos x and sin x. It's not as neat as the one I was going to write about, but I like the video and music, so enjoy..



[link to www.youtube.com (secure)]

K

I was going to go through a very neat proof using polar co-ordinates in the complex plane, but this guy has already done it much better than I could. So here is a second, tidier, proof.



[link to www.youtube.com (secure)]

K

well done on this post- very clever.

There is nothing mysterious nor beautiful about numbers.

Not even i ? A number which is vital in making your TV and radio work, but doesn't even exist at all ?

K

Not being a mathematician, I was highly impressed with Rodin who has over the last thirty five years developed vortex mathematics.

His proofs are visible to non math heads in that he has noted patterns that can be observed by the layman without using too many symbols.

Symbols being for the symbol minded( G Carlin)

I have experience as a musician and electronics tech so I would appreciate e being explained in terms of vortex mathematics.
I am sure the proofs will be there as Euclid is much respected in.electronics as most of it would be impossible without the correct application of e.

I do not want to change the flavor of the post but to create another view,

Who here has the maths to do this.

I first came across Vortex mathematics winding power coils.

Sorry I meant Euler not Euclid.

I don't know anything about vortex mathematics but there has been a close link, through history, between mathematics and music ( and astronomy ) and of course electronics is more of less maths in physical form.

[link to en.wikipedia.org]

It's something Heather Couper was developing a series on.

[link to www.gresham.ac.uk]

K

Heather Couper needs a bigger budget.

Thanks. Here is a link for vortex math.

[link to vortexmath.webs.com]

Great thread!!!

Thanks for that link. I was disappointed that they didn't ask Heather Couper to present the Sky At Night when Patrick Moore died. She is a much better communicator than Chris Lintott. She did a great series for Radio 4 that you can catch here

[link to www.bbc.co.uk]

This is her website ( she shares with Nigel Henbest )

[link to hencoup.com]

K