Euclid - The Father of Geometry
The father of geometry is Euclid. Records show that he lived somewhere around 300 B.C., but that date is sketchy. He was a Greek mathematician and is probably best known for his work Elements. Since little is known about the personal life of Euclid, it is difficult to do a biography on him.
His chief work, entitled Elements, is a comprehensive treatise on mathematics. It includes 13 volumes that entail such subjects as plane geometry, dealing with the properties of flat surfaces and of planar figures, such as the triangle; proportion in general, a particular kind of relation between groups of numbers or quantities; the properties of numbers; in-commensurable magnitudes; and solid geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space. Some people say that the geometrical sections of Elements were actually rearrangements of Exodus previous work. However Euclid himself is said to have made several discoveries in his Number Theory, which is a branch of mathematics that deals with the properties and relationships of numbers.
Most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential thinkers in Western philosophy. Euclid taught geometry in Alexandria and opened a school of mathematics there. He also wrote Data, which was a collection of geometrical theorems; Phenomena, a description of the heavens; and The Division of the Scale, which is a mathematical discussion of music. But yet again many historians believe many of these works (other than the Elements) were spuriously credited to him, others disagree and say that indeed his works are that of his own.
Euclid’s Elements was used as a text for 2000 years, and even today a modified version of its first few books forms the basis of high school instruction in plane geometry. The first printed edition of Euclid’s works was a translation from Arabic to Latin, which appeared at Venice in 1482.
Euclid is called the father of geometry. He has earned the respect from all mathematicians, and is regarded as the creator of the Elements, which is based on almost every point of geometry. Students learn about him every time they open their math book
His chief work, entitled Elements, is a comprehensive treatise on mathematics. It includes 13 volumes that entail such subjects as plane geometry, dealing with the properties of flat surfaces and of planar figures, such as the triangle; proportion in general, a particular kind of relation between groups of numbers or quantities; the properties of numbers; in-commensurable magnitudes; and solid geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space. Some people say that the geometrical sections of Elements were actually rearrangements of Exodus previous work. However Euclid himself is said to have made several discoveries in his Number Theory, which is a branch of mathematics that deals with the properties and relationships of numbers.
Most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential thinkers in Western philosophy. Euclid taught geometry in Alexandria and opened a school of mathematics there. He also wrote Data, which was a collection of geometrical theorems; Phenomena, a description of the heavens; and The Division of the Scale, which is a mathematical discussion of music. But yet again many historians believe many of these works (other than the Elements) were spuriously credited to him, others disagree and say that indeed his works are that of his own.
Euclid’s Elements was used as a text for 2000 years, and even today a modified version of its first few books forms the basis of high school instruction in plane geometry. The first printed edition of Euclid’s works was a translation from Arabic to Latin, which appeared at Venice in 1482.
Euclid is called the father of geometry. He has earned the respect from all mathematicians, and is regarded as the creator of the Elements, which is based on almost every point of geometry. Students learn about him every time they open their math book
Who Discovered "Irrational" Numbers?
The first man to recognize the existence of irrational numbers might have died for his discovery. Hippassus of Metapontum was an Ancient Greek philosopher of the Pythagorean school of thought. Supposedly, he tried to use his teacher's famous theorem to find the length of the diagonal of a unit square. This revealed that a square's sides are incommensurable with its diagonal, and that this length cannot be expressed as the ratio of two integers. The other Pythagoreans believed dogmatically that only positive rational numbers could exist. They were so horrified by the idea of incommensurability, that they threw Hippassus overboard on a sea voyage, and vowed to keep the existence of irrational numbers an official secret of their sect.
There are good reasons to believe Hippassus's demise is merely an apocryphal myth. The primary sources that refer to the incident are both sparse and written 800 years after the time of Pythagoras and Hippassus. That said, a few ancient accounts and their more contemporary embellishments suggest that one of these likely happened:
A Brief History of the Pythagorean Theorem
Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.
Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen. Although he is credited with the discovery of the famous theorem, it is not possible to tell if Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. Unfortunately, this vow of secrecy prevented an important mathematical idea from being made public. The Pythagoreans had discovered irrational numbers! If we take an isosceles right triangle with legs of measure 1, the hypotenuse will measure sqrt 2. But this number cannot be expressed as a length that can be measured with a ruler divided into fractional parts, and that deeply disturbed the Pythagoreans, who believed that "All is number." They called these numbers "alogon," which means "unutterable." So shocked were the Pythagoreans by these numbers, they put to death a member who dared to mention their existence to the public. It would be 200 years later that the Greek mathematician Eudoxus developed a way to deal with these unutterable numbers.
The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.This relationship has been known since the days of the ancient Babylonians and Egyptians, although it may not have been stated as explicitly as above. A portion of a 4000 year old Babylonian tablet (c. 1900 B.C.E.), now known as Plimpton 322, (in the collection of Columbia University, New York), lists columns of numbers showing what we now call Pythagorean Triples--sets of numbers that satisfy the equation
a^2 + b^2 = c^2
Where does ZERO (0) come from?
The concept of Zero is attributed to the Hindus. The Hindus were also the first to use zero in the way it is used today. Some symbol was required in positional number systems to mark the place of a power of the base not actually occurring. This was indicated by the Hindus by a small circle, which was called Shunya, the Sanskrit word for vacant. This was translated into the Arabic Sifr about 800 A.D. Subsequent changes have given us the word zero.In Babylone by middle of the 2nd millenium BC, the lack of a positional value (or zero) was indicated by a space between sexagesimal numerals.
In 498 AD the Indian mathematician and astronomer Aryabhatta stated that Sthanam sthanam dasha gunam means place to place in ten times in value, which may be the origin of the modern decimal-based place value notation. Arabs spread the Hindu decimal zero and its new mathematics to Europe in the Middle Ages.
The concept of Zero is attributed to the Hindus. The Hindus were also the first to use zero in the way it is used today. Some symbol was required in positional number systems to mark the place of a power of the base not actually occurring. This was indicated by the Hindus by a small circle, which was called Shunya, the Sanskrit word for vacant. This was translated into the Arabic Sifr about 800 A.D. Subsequent changes have given us the word zero.In Babylone by middle of the 2nd millenium BC, the lack of a positional value (or zero) was indicated by a space between sexagesimal numerals.
In 498 AD the Indian mathematician and astronomer Aryabhatta stated that Sthanam sthanam dasha gunam means place to place in ten times in value, which may be the origin of the modern decimal-based place value notation. Arabs spread the Hindu decimal zero and its new mathematics to Europe in the Middle Ages.