Fermat's Last Theorem Archives - Math and Multimedia

10 Math Problems That Look Easy But Immensely Difficult to Solve

June 12, 2013 GB High School Mathematics, Problem Solving and Proofs

There are thousands of math problems that are difficult for a common person to understand even though mathematicians may find them easy to solve. On the other hand, there are math problems that look really easy that even a middle student would understand the way they are stated, but their solution or proof is immensely difficult. Yes, such math problems exist and below are the some of the most well known.

1. Squaring the Circle
Squaring the circle is one of the classic math problems proposed by Geometers.
Math Problem: Squaring a Circle It was a challenge to use compass and straightedge to construct a square with the same area as a given circle in a finite number of steps. Although the circle to square approximation was known since the time of the ancient Babylonian mathematicians, it was Anaxagoras (c. 510 – 428 BC) who was the first to be recorded in history to work on the problem.

In 1882, Ferdinand von Lindemann proved that $\pi$ was transcendental. The consequence of this is the impossibility of squaring the circle. » Read more

Understanding the Fermat’s Last Theorem

January 16, 2011 GB College Mathematics, High School Mathematics, Number Theory

The Fermat’s Last Theorem is one of the hardest problems in the history of mathematics. The problem was written by Pierre de Fermat in 1637, and it was only solved more than 300 years later — in 1995 by Professor Andrew Wiles.

But what is exactly the Fermat’s Last Theorem?

The Fermat’s Last Theorem is an extension of the Pythagorean Theorem. Recall that the Pythagorean Theorem states that given a right triangle whose side lengths are $x, y$ and hypotenuse $z$ , $x^2 + y^2 = z^2$ is satisfied. For example, a right triangle with side lengths $2$ , and $3$ has hypotenuse $\sqrt{13}$ .

There are some interesting things that we can see if we examine the side lengths of right triangles. For instance, if we let the triples $(x,y,z)$ be the side lengths of a right triangle, where $z$ is the hypotenuse, we can find triples such that all lengths are integers. The triples $(3, 4, 5)$ , $(5,12,13)$ , $(8,15,17)$ are integer triples, and they satisfy the Pythagorean Theorem. These triples are called Pythagorean Triples. It is not also difficult to see that there are infinitely many Pythagorean Triples (Can you see why?). » Read more

15 comments Andrew Wiles, Fermat's last conjecture, Fermat's Last Theorem, Pierre de Fermat, pythagorean theorem, what is fermat's last theorem

Mathematics and Multimedia Blog Carnival #2

August 9, 2010 GB Blog Carnival, High School Mathematics

Hook, Line and Linker

Welcome to the second edition of the Mathematics and Multimedia Blog Carnival.

One of the new developments is that I am giving a title to each edition of the carnival. The title of second edition: Hook, Line and Linker . As you read, you would know why I have chosen the title.

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