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#51 2012-06-22 13:31:35

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Can you suggest six names of great mathematicians quickly?

Bob was having fun with his, why this Zeckendorf chap is not even a member!

Here is another six:

Doron Zeilberger;
Herbert S. Wilf
Abraham De Moivre of course
Newton of course
Freeman Dyson ( little known )
Pierre De Fermat of course


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#52 2012-06-22 14:00:05

anonimnystefy
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From: The Foundation
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Re: Can you suggest six names of great mathematicians quickly?

Here is a list of some the most known mathematicians:
Euclid
Archimedes
Leonhard Euler
John von Neumann
Pythagoras of Samos
Isaac Newton
Gottfried Wilhelm Leibniz
Rene Descartes
Pierre de Fermat
Carl Friedrich Gauss
Andrey Markov
Evangelista Torricelli
Leonardo Pisano Bigollo (better known as Fibonacci)
Edouard Lucas
Blaise Pascal
Stefan Banach
Srinisava Ramanujan
Brahmagupta (thank you for nothing big_smile)
Evariste Galois
William Rowan Hamilton
Donald Knuth
Doron Zeilberger
Herbert Wilf
Henri Poincare
David Hilbert
Joseph-Louis Lagrange
Bernhard Riemann
Niels Abel
Arthur Cayley
Augustin Cauchy
Georg Cantor
Peter Dirichlet
Diophantus of Alexandria
Pierre-Simon Laplace
Jean le Rond D'Alembert
Francois Viete
Joseph Fourier
Jacob Bernoulli
Simeon-Denis Poisson

There are a lot more great mathematicians, but the ones above should give you a pretty good choice.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#53 2012-06-22 14:37:14

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Can you suggest six names of great mathematicians quickly?

That is a few more than six.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#54 2012-06-22 14:45:38

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

He can still pick the ones he would like. My only mistake is that I haven't included any females in the list. Candidates would be Sophie Germain and S. Bundy.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#55 2012-06-22 16:50:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Can you suggest six names of great mathematicians quickly?

Hypatia
Ada Lovelace


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#56 2012-06-24 14:27:35

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
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Re: Can you suggest six names of great mathematicians quickly?

anonimnystefy wrote:

I tried reading your proof, but my tiny mind couldn't comprehend it.

Me too! May be I will understand some other day when I shall know Mathematics better


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#57 2012-06-24 14:38:38

anonimnystefy
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Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

I just get lost in it. I will have to sit down one day and just read it carefully and thoroughly.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#58 2012-06-24 19:16:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,747

Re: Can you suggest six names of great mathematicians quickly?

Calm down, both of you will get there soon enough!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#59 2012-06-24 21:01:04

bob bundy
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Registered: 2010-06-20
Posts: 6,124

Re: Can you suggest six names of great mathematicians quickly?

I'm supposed to be a teacher.  Eeeekkk!

I'll have another go if you ask me to.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#60 2012-06-25 00:19:46

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

You don't have to trouble yourself, if you ask me. Maybe I am just not careful reading your proof. I will have another go at it later today.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#61 2012-06-25 00:22:02

bob bundy
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Registered: 2010-06-20
Posts: 6,124

Re: Can you suggest six names of great mathematicians quickly?

hi Stefy,

That wasn't the answer I was hoping for.  Perhaps I should have said "I will enjoy trying to make a better explanation".

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#62 2012-06-25 00:23:57

anonimnystefy
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Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

Why would you type up a clearer explanation if the one we have now can be understood with a little bit more effort?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#63 2012-06-25 00:43:30

bob bundy
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Re: Can you suggest six names of great mathematicians quickly?

Because you said you didn't understand it => it wasn't clear.

B


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#64 2012-06-25 00:54:03

anonimnystefy
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Re: Can you suggest six names of great mathematicians quickly?

Incorrect!

I say that it is unclear && I made a reasonable ammount of effort => It is unclear.

And because both conditions aren't met, we cannot claim anything about the clarity of your proof.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#65 2012-06-25 01:05:09

bob bundy
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Re: Can you suggest six names of great mathematicians quickly?

Actually you said your tiny mind couldn't comprehend it.

Since (as a teacher) I have the patience of a saint, I was prepared to spell it out in more simple terms, specifically taking account of your tiny mind.   smile     But if you are rejecting my offer, I'll just seek out someone who appreciates my talent.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#66 2012-06-25 01:17:40

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

Whoa, it seems to me you are twisting my words. I never said that I don't appreciate your talent! If it makes you happy, then, please, present your proof in simpler terms to me.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#67 2012-06-25 01:55:47

bob bundy
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Re: Can you suggest six names of great mathematicians quickly?

Oh thank you!  smile  I'd love to.

The algorithm shows how you can reduce any counting number to a sum of Fibonacci numbers (without repetition).

A number N has an F number subtracted which is saved in a list.

Then the remainder (ie from the subtraction, no division involved) is treated as the new N and the algorithm repeated.

This continues until the remainder is an F; at which point the process stops and the list of subtracted Fs  gives the required sum.

There are three things to prove:

(i) Will it always be possible to find an F to subtract?

(ii)  How do I know that no F is ever subtracted again in the process?

(iii) Will this ever stop?

The key to this is to consider the number N and find the largest F below N and subtract that.

If N is an F already then just stop.

If N isn't an F how do I know I can find an F that is lower?

Well the first three counting numbers {1,2,3} are all Fs, so there is certainly an F that is lower.  If there are several, then pick the biggest!

Let's call that F, 'b'.  And while we are at it, call the one below that, 'a'.

Consider a + b.

It is the next F after b.  Where does it come in relation to N?

Is it equal to N?  If so, then N is an F and we can stop.

Is it below N?  No, because we were told to pick the biggest F below N and call that one 'b'.  So a + b cannot be under N.

So N < a + b     =>   N - b < a

So the remainder from the subtraction is below 'a' and so there is no chance of ever repeating a subtraction of 'b'.  The remainder is just too small.  In fact, we can go further.  Since N - b < a, that means that even 'a' cannot be subtracted from the remainder.  So, having subtracted 'b',  we can never subtract 'a' as well.

So that proves I can find an F and that I'll never repeat an F.

But will I ever stop?

Well the remainders get smaller and smaller whilst remaining positive.  Eventually I'll have to reach an F because the last possible remainders, if no other F presents itself, will be 3 or 2 or 1 and they are all Fs.

So it is guaranteed that I will eventually end in an F.

Example:

N =150

What's the largest Fibonacci number under 150?

144 I think.  That is 'b'.  And 'a' = 89

Calculate N - b = 150 - 144 = 6.  Notice this is under 89.

Replace 150 by 6.

N = 6.  What is the largest F under this?  Answer 5

Calculate N - b = 6 - 5 = 1

This is the new N.  But it is an F so I can stop.

150 = 144 + 5 + 1

Note:  The representation by a sum of Fs is not always unique (150 = 144 + 3 + 2 + 1) but choosing the largest each time is what guarantees that we don't repeat and we don't get two consecutive Fs.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#68 2012-06-25 02:42:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

Now that is simple. I understood it this time.

I have a little problem with your note in the end. Again, the Zeckendorf theorem states that every number has a unique representation as a sum of non-adjacent Fibonacci numbers. Your proof takes care of that, but your comment at the end ruins it. Just a little notice from me. smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#69 2012-06-25 04:48:15

bob bundy
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Registered: 2010-06-20
Posts: 6,124

Re: Can you suggest six names of great mathematicians quickly?

Sure it does.  But I wasn't trying to prove that theorem, just show the representation is possible.  And that statement emphasises why the largest is needed at each stage.  (challenge:  Find a number with more than one representation that does satisfy the theorem.)

Thanks for reading it and allowing me the chance to show off some more.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#70 2012-06-25 05:24:31

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

Do you want me to find a number which can be represented as a sum of several non-adjacent F numbers in two different ways?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#71 2012-06-25 06:02:22

bob bundy
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Registered: 2010-06-20
Posts: 6,124

Re: Can you suggest six names of great mathematicians quickly?

Yes, if you can.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#72 2012-06-25 06:10:30

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Can you suggest six names of great mathematicians quickly?

That is impossible. The impossibility is proven by the Zeckendorf theorem.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#73 2012-06-27 16:33:07

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

Re: Can you suggest six names of great mathematicians quickly?

Thank You,
Bob


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#74 2012-10-07 20:10:14

Mark-nz
Member
Registered: 2012-10-07
Posts: 3

Re: Can you suggest six names of great mathematicians quickly?

Thales, Archimedes, Eudoxus, Euclid, Diophantus, Newton are six pretty prominent guys.

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#75 2012-10-08 11:19:52

ShivamS
Member
Registered: 2011-02-07
Posts: 3,415

Re: Can you suggest six names of great mathematicians quickly?

I cannon believe no one suggested Gottfried Wilhelm Leibniz, possibly the greatest mathematician of all time and the original creator of Calculus.

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