Euclidean geometry summary

David Hilbert was a German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundations of mathematics. His work in 1909 on integral equations led to 20th-century research in functional analysis. The first steps of

Euclid was the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements. Of Euclid’s life nothing is known except what the Greek philosopher Proclus (c. 410–485 ce) reports in his “summary” of famous Greek mathematicians. According to him, Euclid

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2. Although the theorem has long been associated with Greek