The study of geometrical figures and shapes which is based on various theorems and axioms is called Euclidean geometry. The type of geometry mainly applies for flat surfaces. It helps in explaining the shapes of geometrical figures better, particularly the plane figures. Greek mathematician Euclid had described ‘Euclidean geometry’ in his book ‘Elements’. Through the book, he introduced the fundamentals of geometry comprising geometrical figures and shapes. He had also stated the five main postulates and axioms which are regarded as universal truths. However they are yet to be proved!
Euclid, an ancient Greek mathematician from Alexandria (Ptolemaic Egypt) wrote his mathematical and geometrical work in a total of 13 books. It came to be known as Euclid’s Elements. The ‘thirteen’ books popularized geometry across the globe. In short, Euclid Elements is a compilation of postulates, axioms, definitions, theorems and constructions. It also includes mathematical proofs of the propositions as well.
Plane Geometry is primarily discussed in book 1 to 4th and also 6th. The five postulates which were given by Euclid were called Euclid’s Postulates. The geometry is popularly known as Euclidean geometry. Euclid’s works laid the foundation for geometry.
Leonard Mlodinow was the author of Euclid’s Window (the story of geometry from parallel lines to hyperspace). The American theoretical physicist explained geometry with the Greek concept of parallel lines, up to the latest notions of hyperspace.
The seven Euclid axioms are:
- Things which are equal to identical things are also equal to each other.
- If equals of something are added to equals, then as a whole, they will be considered as equals.
- If equals of something are subtracted from equals, then their reminders will also be equal.
- Things which coincide with each other are equal.
- The whole of something will be greater when compared to the ‘part’.
- Things which are double of identical things will be equal to each other.
- Things which are halves of identical things will be equal to each other.
Euclid’s postulates are:
- A straight line can be drawn from any one point to the other.
- A terminated line can be generated indefinitely.
- A circle can be drawn by choosing any center and also any radius.
- All right angles will be equal.
- When a straight line falling on 2 straight lines forms the interior angles on the same side of it taken together less than two right angles, then the 2 straight lines, if generated indefinitely, meet on that side on which the sum of angles will be less than two right angles.
Answer) The study of geometrical figures and shapes which is based on various theorems and axioms is called Euclidean geometry.
Answer) Euclid’s Elements.
Answer) Leonard Mlodinow.