Understanding the Fermat’s Last Theorem

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

Miscellaneous GeoGebra Links

Here are some excellent resources that you can use if you are teaching and learning GeoGebra. Official Web Page

Tutorials & Workshops

GeoGebra Basic Construction 7 – Rhombus

This is the seventh tutorial in the GeoGebra Basic Construction Series. If you are not familiar with GeoGebra, you may want to read the Introduction to GeoGebra post and prior tutorials in the series. They contain the pre-requisites of this tutorial.

In the tutorial below, menu commands, located in the menu bar, are in green bold text, and submenus are denoted by the > symbol. For example, Options>Labeling> New Points Only means, click the Options menu, choose Labeling from the list, then select New Points Only. The tool texts are colored orange. For example, New Point means the new point tool.

In this tutorial, we construct a rhombus using a circle. Although, we have already discussed how to construct a rhombus,  the method used in this  construction is different.  In this tutorial, we construct a rhombus mimicking compass and straightedge construction.

Rhombus - GeoGebra

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