Why Euclid is known as the Father of Geometry

Geometry is a significant branch of mathematics that deals with the study of shapes, sizes, and dimensions of figures. Introduced by the Greeks, it is one of the mandatory subjects taught in schools these days. And while some students find the subject interesting, others may have trouble understanding it.

Geometry has a long history, and the person who is regarded as its originator is Euclid. There are many reasons why, and we will explain them all so you will know why Euclid is known as the Father of Geometry. 

Who was Euclid?

Euclid, famously called the “Father of Geometry,” is a Greek mathematician from Egypt. He is believed to have been born around the third century BC in the Greek city of Alexandria, where he spent the major part of his life teaching mathematics to young people. He prominently taught students and developed the concepts of geometry, from which the subject still owes most of its basics.

The information on Euclid’s personal life is meager, and historians have come to know most about him through the works of Greek philosophers like Proclus. Euclid is well known to students as a part of their math books, and most of the information available about him is related to his contribution to mathematics. Besides math, the name Euclid is also common in history and scientific texts.

What did Euclid do?

Alongside being a great mathematician, Euclid is also referred to as one of the greatest thinkers of all time. He wrote “Elements,” a text containing 13 sections of a detailed study of various mathematical disciplines. It incorporated subjects like plane geometry, solid geometry, 3D geometric figures, proportion, disproportionate lines, and number theory. 

Euclid presented different theories, definitions, and developments in Mathematics of his time in “Elements,” which have proven to be useful even today. He used logic to prove every theorem that later shaped the ideas of western philosophers. While his work is praised worldwide, some believe that several sections of his work are a mere accumulation of the ideas of other mathematicians, such as the Exodus, Pythagoras, Theudius, and others. The rest think that the discoveries included in the text are his own.

Euclid’s “Elements” contains 465 theorems and proofs, which are properly described with the required diagrammatical construction. The creation of “Elements” that popularized certain portions of geometry is called Euclidean Geometry. He also wrote what is called “Data,” a comprehensive collection of geometrical theorems, phenomena, and the division of the scale. But just like in “Elements,” historians doubt the authenticity of these works and feel that they might be the ideas of other mathematicians. He was also the first to describe the Golden Ratio in terms of ratios and to show its appearance in a variety of geometric shapes.

In 1482, the first printed copy of Euclid’s work was found in Venice. The impact of his work is extraordinary, as it is considered important to the present day and holds relevance to the context of present mathematics. The 2000-year-old text constitutes the basics of geometry that every student learns in their initial days of school. Thus, Euclid is considered the “Father of Geometry.”

Some of Euclid’s notable theories are:

• The Number Theory
• The Fundamental Theorem of Arithmetic
• The Euclidian Geometry

Euclid’s Achievements & Contributions to Geometry

Even after all the noteworthy concepts Euclid developed, he is best known for his contributions to geometry. His famous work, ‘Elements,’ contained five general axioms and five geometric postulates that served as a model for mathematical argument, allowing theorems to be established using logical deductions from initial assumptions. Sir Thomas Heath summarized Euclid’s axioms and postulates in his 1908 publication, “The Elements of Euclid.”

Euclid’s 5 General Axioms:

1. Things that are equal to the same thing are also equal to one another.
2. If equals are added to equals, the wholes (sums) are equal.
3. If equals are subtracted from equals, the remainders (differences) are equal.
4. Things that coincide with one another are equal to one another.
5. The whole is greater than the part.

Euclid’s 5 Geometric Postulates:

1. It is possible to draw a straight line from any point to any point.
2. It is possible to extend a finite straight line continuously in a straight line.
3. It is possible to create a circle with any center and distance.
4. All right angles are equal to one another.
5. If a straight line falls on two straight lines, making the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side where the angles are less than two right angles.

These axioms and postulates are still used to this day to prove theorems and solve geometrical problems. 

The many theories, definitions, and concepts of mathematics, as provided by Euclid, are a significant part of the subject. They have provided the students with the basics of knowledge and helped mathematicians after him solve advanced problems, demonstrating Euclid’s greatness as a mathematician. 

With this blog by BYJU’S FutureSchool, we tried to inform you about the origins of geometry and the person who fathered it. So now, let us know in the comments if you like geometry and your views on it.