exp-function

Two functions meet in a narrow street.

F1: Clear the way!
F2: No, I won't.
F1: Move over, or I will differentiate you!
F2: Ok, try it, I am the exp-function!

Available: http://www.primepuzzle.com/leeslightest/mathjokes.htm

Noah and his Ark

The ark lands after The Flood. Noah lets all the animals out. Says, "Go and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly", say the snakes. "We're adders, and we need logs to multiply."

Available: gopher://wiretaps.spies.com/00/Library/Humor/Jokes/math.jok

Definition: Mathematician

"A mathematician is a device for turning coffee into theorems" -- P. Erdos

Famous curves - Lituus

The lituus curve originated with Cotes in 1722. Lituus means a crook, for example a bishop's crosier. Maclaurin used the term in his book Harmonia Mensurarumin 1722. The lituus is the locus of the point P moving in such a manner that the area of a circular sector remains constant.
Roger Cotes (1682-1716) died at the age of 34 having only published two memoirs during his lifetime. Appointed professor at Cambridge at the age of 24 his work was published only after his death.
Cotes discovered an important theorem on the nth roots of unity; anticipated the method of least squares and discovered a method of integrating rational fractions with binomial denominators.

(1997. Available: http://www-history.mcs.st-andrews.ac.uk/history/Curves/Lituus.html )

The basics

Ever think back to when you had your first encounter with mathematics?

Or what about those high school exams?

I think when some of us look back to those days we realize how little of mathematics we knew then (and still do). That was only a drop in the big ocean, with still so much that is unexplored. This is one of the many reasons why I love math, there's always new things to learn and discover, you definitely can never get bored or run out of ideas, there is always excitement.

Although some people would read my last statement and think: "Nerd!" or "Geek!", I feel obliqed to feel sorry for them, because there is this amazing,, incredible thing in life that they would probably never discover.

I am not saying that everyone should love or even like math, but it is definitely something which should be appreciated.

Mathematics is everywhere imaginable, it is infinite.

HAVE FUN

Pythagoras

The picture below is indeed of Pythagoras.

For more about him please visit this link:

http://www-history.mcs.st-andrews.ac.uk/Biographies/Pythagoras.html

Who is this?

Born: about 569 BC in Samos, Ionia
Died: about 475 BC

Mathematician: Ahmes

Ahmes:

• Born: about 1680 BC in Egypt
• Died: about 1620 BC in Egypt

Ahmes is the scribe who wrote the Rhind Papyrus (named after the Scottish Egyptologist Alexander Henry Rhind who went to Thebes for health reasons, became interested in excavating and purchased the papyrus in Egypt in 1858).
Ahmes claims not to be the author of the work, being, he claims, only a scribe. He says that the material comes from an earlier work of about 2000 BC.
The papyrus is our chief source of information on Egyptian mathematics. The Recto contains division of 2 by the odd numbers 3 to 101 in unit fractions and the numbers 1 to 9 by 10. The Verso has 87 problems on the four operations, solution of equations, progressions, volumes of granaries, the two-thirds rule etc.
The Rhind Papyrus, which came to the British Museum in 1863, is sometimes called the 'Ahmes papyrus' in honour of Ahmes. Nothing is known of Ahmes other than his own comments in the papyrus.

Article by: J J O'Connor and E F Robertson
January 1997
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Ahmes.html]

Answer to integral

This is indeed true and it is also a limerick:

Integral t-squared dt

from 1 to the cube root of 3

times the cosine

of three pi over 9

equals log of the cube root of 'e'.

(a limerick is poem with the 1st, 2nd and 5th lines rhyming and also the 3rd and 4th lines rhyming - just comes to show what one can do with mathematics)

Limits

Introduction: Mathematicians

The first mathematicians I’m going to take a look at are some of those who lived -500 AD. Yes, that’s a very long time ago, at the origin of the discovery of mathematics.
(Take note that it cannot be the origin of mathematics, because I don’t think there really is something like that, mathematics was always present, only people weren’t aware of it.)
I’m planning on then looking at the 1800’s and then again further back, to create some kind of oscillating effect.
I hope that those of you who will read it will find it interesting.

Mathematicians

I will do my best to start publishing information and theories of mathematicians, especially those who contributed greatly to mathematics as we know it today.
I believe that it is important to know about these minds behind the ideas and theories, so that we can in a sense understand it better and also catch a glimpse of some truly dedicated mathematicians.
Althought there are many famous and well-known mathematicians, I also believe that there are many more out there who just wasn't in the right place and time to be truly recognised for the work they have done.
I also think that there must have been times when some mathematicians got credit for work which has already been done and proven by someone else who didn't make it public, or just kept it to themselves. Althought this is truly sad, we nevertheless can and will benefit from those proofs and theories, irrespective of who are known for it, and build on that to, hopefully, discover even more.

Life is a journey, and so is mathematics.

How does that work?

A classic example of how one can easily be misled by mathematics when one doesn’t have efficient knowledge to know better.
2a = a, does in fact not mean that 2 = 1, but rather that a has a value that would satisfy 2a = a. Therefore a = 0 is the only possibility.

Question: Integration

True or false?
To be continued...

Expand

No, this is not how it is done.
Really.
Still don’t believe me? I guess then you’re still stuck with high school math?
Anyway, don’t we all just miss high school math? So carefree and fun! (Well, for some of us at least.)
For originality, I must give Peter 10 out of 10.

Proof: Mathematics is Art

Prove by induction:

Note: Weird person: the way other people see for example mathematicians or artists.

Consider 1 weird person: This person is thus either an artist or mathematician.
Assume for k weird persons: Each one is either artist or mathematician.
Thus for k +1 people = k persons + 1 person: Either artist or mathematician.

Hence:
We have now proven that mathematicians and artists are not clearly distinguishable, and thus math and art are very closely related. Nearing infinity, they tend to be the same thing.
Now we can say that math is art. (Under the condition that our conclusion can never be commutative, i.e. art is not math!)

Mathematics is an Art!

Creativity, Ideas = Art

• When we think art, we think crazy people in weird outfits, with splatters of paint all over them, creating strange, often beautiful, images.


• When we think math, we think weird people, wearing glasses, working out equations the entire day.
  

See the comparison? Weird people, wrong assumptions made by others, the creation of something great and beautiful...

By induction it can thus be proven that math is indeed an art. (I will provide the proof in the next post).

Definition of pi

What is "pi"?
Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.
Physicist: Pi is 3.1415927 plus or minus 0.00000005
Engineer: Pi is about 3.

(URL: http://www.primepuzzle.com/leeslightest/mathjokes.htm)

Definition of Mathematics

Faced with the question of what the definition of mathematics is got me thinking... And to tell you the truth, I am still thinking.
Can such a vast field ever be pinned down to one specific definition?
Consider infinity, now try to capture that into one thing... Okay, so it's got a name, but the definition of that name is also kind of, uhm, infinite?
So many things still to be proven, discovered and studied, I don't really believe that there can be a definition of mathematics.
Care to differ? Feel free to give your opinion.
I found this definition at http://www.allnewuniverse.com/:
A great language and like any language may be used to describe emotions as well as ideas - truths and philosophies - facts and fiction. We must be very alert to distinguish what math is telling us. Math by itself is not fact!

How they prove that all odd integers higher than 2 are prime?

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime,...
Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime,...
Programmer: 3 is a prime, 5 is a prime, 7 is a prime, 7 is a prime, 7 is a prime,...
Salesperson: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- we'll do for you the best we can,...
Computer Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,...
Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet,...
Advertiser: 3 is a prime, 5 is a prime, 7 is a prime, 11 is a prime,...
Lawyer: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- there is not enough evidence to prove that it is not a prime,...
Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.
Statistician: Let's try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime...
Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
Computational linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime,...
Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,...

(www.workjoke.com)