Euclidean Geometry: Definition, History & Examples

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  • 0:03 Origins of Euclid's Geometry
  • 0:41 Basics of Euclidean Geometry
  • 1:47 Euclid's Legacy
  • 2:59 Lesson Summary
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Lesson Transcript
Instructor: Erin Tigro
The lesson will explore the history and nature of Euclidean geometry, including its origins in Alexandria under Euclid and its five postulates. Its influence on the work of other mathematicians will also be covered.

Origins of Euclid's Geometry

During the fourth and third centuries B.C.E., an Alexandrian Greek named Euclid wrote The Elements, in which he laid down the foundations for working with various two-dimensional and three-dimensional shapes in a study now called geometry. Although most of what he wrote had been discovered before by other mathematicians. Euclid was important because he was the first person to systematize all of the previous observations on geometry into a single coherent system. It was called Euclidean geometry in his honor, though today it is also known as plane geometry, or the study of shapes on flat surfaces.

Basics of Euclidean Geometry

Euclid began his study with what he knew to be true, including the transitive, addition, and subtraction properties of equality, the reflexive property; and the notion that the whole is greater than any part.

He also had five postulates:

  1. Any two points can be joined to form a straight line segment.
  2. Any straight line segment can be extended indefinitely in a straight line.
  3. Given any straight line segment, a circle can be drawn having the segment as a radius and one endpoint as its center.
  4. All right angles are congruent.
  5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than the two right angles, then the two lines must inevitably intersect on that side if extended far enough.

With these elements in place, Euclid proceeded to lay out a systematic study of geometry using his self-apparent statements and postulates as a foundation.

Euclid's Legacy

The importance of Euclid's work was immediately apparent. Archimedes (287-212 BCE) added to the work by working out proofs for the area and volume of various shapes and formulated the Archimedean proof of finite numbers, based on Euclid's work. Apollonius of Perga (262-190 BCE) explored conic sections.

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