Euclid of Alexandria, a Greek mathematician active around 300 BC, is known as the 'father of geometry' and authored 'Elements', a foundational text in mathematics that shaped the study of geometry for centuries. While little is documented about his life, his work introduced a coherent framework for mathematics that includes rigorous proofs and various mathematical concepts, such as number theory and geometric constructions. Five of Euclid's works survive, covering topics from geometry to optics, and he is recognized for his significant influence on the development of mathematics through history.

1. Who is Euclid?

2. Euclid of Alexandria
"Euclid" is the Greek name, meaning "Good Glory".
Euclid - 300 BC, also known as Euclid of Alexandria, was
a Greek mathematician, often referred to as the "Father
of Geometry".
He was active in Alexandria during the reign of Ptolemy I
(323–283 BC).
His Elements is one of the most influential works in the
history of mathematics, serving as the main textbook for
teaching mathematics (especially geometry) from the
time of its publication until the late 19th or early 20th
century.

3. Surviving Fragments
One of the oldest surviving fragments of Euclid's Elements, found at
Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram
accompanies Book II, Proposition 5.

4. Euclid's life
Little is known about Euclid's life, as there are only a
handful of references to him.
It is believed that Euclid may have studied at Plato's
Academy in Athens.
King Ptolemy asked if there was a shorter path to learning
geometry than Euclid's Elements, "Euclid replied there is
no royal road to geometry.“
Apollonius "spent a very long time with the pupils of
Euclid at Alexandria, and it was thus that he acquired
such a scientific habit of thought."

5. Painting History
Euclid in Raphael's School of Athens

6. Elements and Euclid
Although many of the results in Elements originated with
earlier mathematicians, one of Euclid's accomplishments
was to present them in a single, logically coherent
framework, making it easy to use and easy to reference,
including a system of rigorous mathematical proofs that
remains the basis of mathematics even today.
The only reference that historians rely on of Euclid having
written the Elements was from Proclus, who briefly in
his Commentary on the Elements ascribes Euclid as its
author.

7. Euclid through pictures

8. Elements and number theory
The Elements also includes number theory. It considers
the connection between perfect numbers and
Mersenne primes, the infinitude of prime numbers,
Euclid's lemma on factorization (which leads to the
fundamental theorem of arithmetic on uniqueness of
prime factorizations), and the Euclidean algorithm
for finding the greatest common divisor of two
numbers.

9. Euclid through pictures

10. Euclidean geometry
The geometrical system described in the Elements was
long known simply as geometry, and was considered
to be the only geometry possible. Today, however,
that system is often referred to as Euclidean
geometry to distinguish it from other so-called non-
Euclidean geometries that mathematicians
discovered in the 19th century.

11. Dodecahedron
Euclid's construction of a regular dodecahedron

12. Other works of Euclid
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.
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 given ratios. It is similar to a third
century AD work by Heron of Alexandria.

13. Other works of Euclid..
3. Catoptrics, which concerns the mathematical theory of mirrors,
particularly the images formed in plane and spherical concave
mirrors. The attribution to Euclid is doubtful. Its author may have
been Theon of Alexandria.
4. Phaenomena, a treatise on spherical astronomy, survives in Greek;
it is quite similar to On the Moving Sphere by Autolycus of Pitane,
who flourished around 310 BC.
5. Optics is the earliest surviving Greek treatise on perspective. In its
definitions Euclid follows the Platonic tradition that vision is caused
by discrete rays which emanate from the eye. One important
definition is the fourth: "Things seen under a greater angle appear
greater, and those under a lesser angle less, while those under equal
angles appear equal."

14. Critics
His (Euclid) definitions do not always define, his
axioms are not always indemonstrable, his
demonstrations require many axioms of which he is
quite unconscious. (Bertrand Russell, The Teaching of
Euclid, The article appeared in The Mathematical Gazette in
1902. The Nobel Prize in Literature 1950)
Mathematics, rightly viewed, possesses not only truth,
but supreme beauty - a beauty cold and austere, like
that of sculpture. (Bertrand Russell)

15. Poem about Euclid

16. Further research
Alexander the Great founded some twenty cities that bore his
name, most notably Alexandria in Egypt. Alexander died in
Babylon in 323 BC.
Alexander crossed the Indus and fought and won an epic battle
against King Porus (Purushottama), who ruled a region in the
Punjab, in the Battle of the Hydaspes in 326 BC. Alexander
was impressed by Porus's bravery, and made him an ally.
In the aftermath of Alexander's conflicts in North-Western India,
Megasthenes' Herakles who travelled to India as the
ambassador of the Seleucids during the reign of Chandragupta
Maurya.

17. Further research..
Dionysius was a Greek of the 3rd century BCE, who was sent as
ambassador to the court of the Indian emperor Ashoka, by
Ptolemy Philadelphus.
He was preceded in this role by Megasthenes, ambassador to
Chandragupta Maurya, and Deimachus, ambassador to his son,
and father of Ashoka, Bindusara.
It is possible that these Ambassadors, led by scholars from the
ancient Greek empire, learned from the Indian Universities /
Scholars and transferred our ancient wisdom (including
Surgery from Ayurveda, Matahematics from Jyothisha and
Philosophy from the Vedas) which later became the ancestral
property of the Western world.

18. Project work
• Compiled by Mrs. Sreeja MK, student of Teachers'
Education (B.Ed.) Programme 2011-12, Mahathma Gandhi
University, Kottayam
sreeja.thannikat@gmail.com 0481 – 2 393 120
• Mahatma Gandhi University College of Teacher Education,
Kudamaloor, Govt.High School Campus, Kudamaloor, Kottayam,
Tel.No. 0481 – 2 391 264.