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GEObject
Compass-and-ruler geometry

GEObject makes it possible to study and experiment Euclidean Geometry.

Ever since ancient times mathematicians have had to solve geometrical problems and find general properties of geometrical figures: showing a possible solution to a problem often meant providing a construction as the concept of formal proof came only later.

Euclid and other geometers formalized the process of building a geometrical construction, adopting specific tools.
In particular, there had been a debate among geometers about which were the minimal required tools needed to draw given set of figures: compass and ruler, only a ruler, only a compass and so on.

The Compass-and-ruler geometry is that field of the classical geometry that requires the use of only a compass and a ruler, and thus allows to construct those geometrical objects that Galois proved to be those and only those that can be expressed in term of algebraic equations that can be solved by applying a finite number of rational operations or second order radicals.

The ruler allows to draw the segment that joins two given points or the line passing through two different points; the compass allows to describe a circumference or an arc with given center and radius.

Therefore now we know that not all constructions can be solved by using only compass and ruler. For instance the famous problem of trisecting an angle or finding the square of double area of a given square are not solvable by construction with those tools.
A problem is defined as elementary solvable when it's possible to solve it using compass and ruler only, and it's defined not elementary solvable if the solution required other tools.

Even so, the compass-and-ruler paradigm is a very important field of modern geometry, and it's useful in the educational area.