I. Greek Mathematicians
Thales of Miletus
Birthdate: 624 B.C.
Died: 547-546 B. C.
Title: Regarded as “Father of Science”
* He is credited with the first use of deductive reasoning applied to geometry. * Discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. * Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research. * Thales theorems used in Geometry:
1. The pairs of opposite angles formed by two intersecting lines are equal. 2. The base angles of an isosceles triangle are equal.
3. The sum of the angles in a triangle is 180°.
4. An angle inscribed in a semicircle is a right angle.
Birthdate: 569 B.C.
Died: 475 B.C.
* Pythagorean Theorem. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides.
Note: A right triangle is a triangle that contains one right (90°) angle. The longest side of a right triangle, called the hypotenuse, is the side opposite the right angle. The Pythagorean Theorem is important in mathematics, physics, and astronomy and has practical applications in surveying. * Developed a sophisticated numerology in which odd numbers denoted male and even female: 1 is the generator of numbers and is the number of reason
2 is the number of opinion
3 is the number of harmony
4 is the number of justice and retribution (opinion squared) 5 is the number of marriage (union of the ﬁrst male and the ﬁrst female numbers) 6 is the number of creation
10 is the holiest of all, and was the number of the universe, because 1+2+3+4 = 10.
* Discovery of incommensurate ratios, what we would call today irrational numbers. * Made the ﬁrst inroads into the branch of mathematics which would today be called Number Theory. * Setting up a secret mystical society, known as the Pythagoreans that taught Mathematics and Physics.
Birthdate: 500 B.C.
Died: 428 B.C.
* He was the first to explain that the moon shines due to reflected light from the sun. * Theory of minute constituents of things and his emphasis on mechanical processes in the formation of order that paved the way for the atomic theory. * Advocated that matter is composed of infinite elements. * Introduced the notion of nous (Greek, “mind” or “reason”) into the philosophy of origins. The concept of nous (“mind”), an infinite and unchanging substance that enters into and controls every living object. He regarded material substance as an infinite multitude of imperishable primary elements, referring all generation and disappearance to mixture and separation, respectively.
Birthdate: c. 335 B.C.E.
Died: c. 270 B.C.E.
Title: “Father of Geometry”
* Published a book called the “Elements” serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.
The Elements. One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100.
* Wrote works on perspective, conic sections, spherical geometry, number theory and rigor. * In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions. Those are the following:
1. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. 2. On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in...
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