Euclid: Father of geometry

Euclid: Father of geometry

Introduction

●   Euclid sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

●   He was active in Alexandria during the reign of Ptolemy .

●   His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics  from the time of its publication until the late 19th or early 20th century.

●   In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms.

Biography of Euclid

➢      Arabic authors concluded Euclid came from a rich background.➢      His Father was "Naucrates," and his Grandfather was Zenarchus.

      ➢      It is said that he was a Greek born in Tyre and lived in Damascus throughout his life.

      ➢      However, there is no certain evidence if he was the same person as Euclid of Alexandria is often confused with Euclid of Megara, another man who was a philosopher and lived at the time of Plato.

career

★  Euclid’s ‘Elements’ is considered as one of the most influential works in the history of mathematics, from the time of its publication until the late 19th or early 20th century.

★  It actually served as the main textbook for teaching mathematics during this period.

★   In his Elements, he deduced the principles of ‘Euclidean geometry’ from a small set of axioms

★   Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

★   In addition to his most famous work ‘Elements’, there are at least five works of Euclid that have survived to this day.

★  They seem to follow the same logical structure as followed in Elements. They are ‘Data’, ‘On Divisions of Figures', 'Catoptrics', 'Phaenomena' and 'Optics'.

Euclid’s Axioms

1.Given two points there is one straight line that joins them.

2. A straight line segment can be prolonged indefinitely.

3. A circle can be constructed when a point for its centre and a distance for its radius are given.

4. All right angles are equal.

5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles.

Euclid's common notions

6. The objects equal to the same things are equal.

7. If equals are added to equals, the wholes are equal.

8. If equals are subtracted from equals, the remainders are equal.

9. The same objects  coincide with one another .

10. The whole is greater than a part. 

Euclid Elements

❖      Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios not to be confused with the physician Hippocrates of Cos.

❖      The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle .

❖      The older elements were at once

❖      superseded by Euclid’s and then forgotten.

❖      For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids.

Euclid Father of geometry

➔  Euclid was an ancient Greek mathematician in Alexandria, Egypt. Due to his groundbreaking work in math, he is often referred to as the 'Father of Geometry'.

➔  It presents several axioms, or mathematical premises so evident they must be true, which formed the basis of Euclidean geometry.

Euclidean Geometry

○   Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

○   Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions.

Some quotes of Euclid

➔      The laws of nature are but the mathematical thoughts of God.” ...

➔      “There is no Royal Road to Geometry.” ...

➔      “What has been affirmed without proof can also be denied without proof.” ...

➔      “Handwriting is a spiritual designing, even though it appears by means of a material instrument.” ...