Euclid: The Father of Geometry

Euclid is considered by many to be the father of reason and intellect, advancing mankind from appeals to the gods to the application of the thinking faculties.

The truth is that he built on the work of centuries of Greek thinkers including Thales of Miletus and Anaximander. Yet it was Euclid who encapsulated their approach to thinking in such a thorough and foolproof way that its lasting adoption was guaranteed.

We don’t know much about the life of Euclid the man. It is believed that he lived around 300 BCE in the great Egyptian city of Alexandria. That city, founded a few decades earlier by Alexander the Great, was home to a huge Museum and Library, the greatest educational institution in the world at that time.

Euclid was a teacher of mathematics at Alexandria. It is possible that he was a student of Plato. Several anecdotes have survived to give us glimpses into his character. One source described him as being …

most fair and well disposed towards all who were able in any measure to advance mathematics,
careful in no way to give offense, and although an exact scholar never vaunting
himself.

A story is related to how Egyptian ruler King Ptolemy asked Euclid if he had to read the whole of his landmark book on geometry Elements to learn the subject. In response, Euclid is supposed to have said …

There is no royal road to geometry.

So little is known about the life of the man that it has been suggested that the name Euclid is actually the name that a group of Alexandrian mathematicians gave to themselves when publishing Elements. Still, whether it was written by one man or many, there is no doubt that Elements is one of the most important books ever written.

Elements are basically about geometry, the study of shape. It contains all of the basic rules to do with triangles, squares, rectangles, and other shapes that children are taught in school today. But the book did more. It quantified a whole new way to think - one that was based upon logic, deductive reading, evidence, and proof. By using these methods people could uncover the natural rules that governed the workings of the world.

Euclid’s great accomplishment was not in the uncovering of new facts about new geometric shapes, but in combining geometrical theorems into a coherent framework of basic theory and proofs. This is the basis of modern science.

By turning mathematics into a logical system, Euclid gave it extraordinary power. He introduced the idea of proofs and the idea that rules could be worked out logically from certain assumptions. Assumptions could then be combined to create a theorem.

The 5 key axioms in Euclid’s Elements are …

Part of a line can be drawn between two given points.
2. Such a part line can be extended indefinitely in either direction.
3. A circle can be drawn with any radius with any given point at its center.
4. All right angles are equal.
5. If part of a line crosses two other lines so that the inner angles on the same
sides add up to less than two right angles, then the two lines it crosses must eventually meet.

With these watertight definitions, it was possible to establish firm proofs of otherwise vague hunches. The last of Euclid’s axioms - if part of a line crosses two other lines so that the inner angles on the same side add up to exactly two right angles, then the two lines it crosses must be parallel - is called the parallel postulate. It was held a basic central truth but Euclid was not entirely happy with it.

He was right to have reservations. Euclidean geometry works perfectly on flat surfaces. Just as the Earth’s surface is not actually flat, however much it appears to be, space is actually curved and has many more than three dimensions, including that of time.

Euclid's parallel postulate means that only one line can be drawn parallel to another
through a given point, but if space is curved and multidimensional, many other
parallel lines can be drawn. Similarly, according to Euclid’s geometry, the internal
angles of a triangle always add up to 180 degrees – yet those of a triangle drawn on a ball add up to more than 180.

It wasn’t until the 19th century that mathematicians such as Carl Gauss began to realize the limitations of Euclidean geometry and develop new geometric concepts to cover curved space. Yet, the work that Euclid did in the 3rd century BCE has formed the foundation of geometry for more than 2 millennia. Even more profoundly, his insistence on establishing truth by water-tight reasoning based on logic, deduction, evidence, and the proof has been the bedrock of every advancement through history.

Credits:
Script - Steve Theunissen
Voice Actor - James Fowler

[thehussarsjacobitess]

Beautiful! I love how you brought out Euclid's own reservations regarding the pure abstraction of what he was doing and the later problems that modern geometry would resolve. :)

[dharialurie]

"The Pledge

Life was bestowed upon man by the Creator
The ways of tradition were by Him laid down
In following them we may discover His path,
and return to Heaven, made pure
With the loss of tradition goes our humanity
Modern ways of thinking are a morass most deep
The doctrines of atheism and evolution
are promulgated at the Devil Red’s decree
Most human lives were divine before coming here,
and with the Creator a pledge made
True glory lies in discovering His way, doing
spiritual practice, and forging a body divine
For you once promised to bring salvation
to your own Kingdom and its many lives

February 26, 2018"
Master Li Hongzhi (Hong Yin VI, from Falun Dafa teachings)

[alifakhan]

Thank this video is very helpfull for my future

[rickybosephus]

I wasn't taught that the Greeks did this. We need to give credit to Greeks and this book, "Elements"

[normdurkin]

mathematics in eurorack modular synthesis modules brought me here..

[dharialurie]

"What Our Lives Hope For

Most people are divinities incarnate,
here to await the Creator
But over all the many lifetimes
vows were forgotten and outlooks changed
The way back to Heaven has been blazed,
though it is shrouded in mist
Man’s warped thinking and conduct
spells ruin for posterity
The doctrines of atheism and evolution
are doing humanity harm
But the Creator now has the Devil Red,
Satan, pinned underfoot
And it is at His command that
followers of Dafa [Great Law] strive to save lives
Discover the truth to clear away
whatever may impede your salvation

January 31, 2018"
Master Li Hongzhi (Hong Yin VI, from Falun Dafa teachings)

[thespartan]

I am Hellen, not Greek. There is an intelligent video to be made in English about Euclid culture, and this isn't it.
You shouldn't approach this video as history in the typical sense. Treat it as an interesting speculative documentary with some historical information thrown in.
History is way more clear with a Hellenic classical education, and someone who speaks like a native Greek and not as an outsider/foreigner who learned Greek.

No other small country can compare with Greece in terms of impact on human benefit.
In the beginning... God created the Earth, and in the light blue waters, put a small ship to travel forever, in order not only to give birth but also to transfer great ideas all over the world ...
He called that ship...HELLAS! 🐬

The only good is knowledge, and the only evil is ignorance. Herodotus.

[ptahsekhemtehuti]

This universe doesn’t work off lines but curvature

[MoneyG]

Topography is the study of shape not Geometry