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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Geometry can be traced all the way back to 2000 BC. Watch this video lesson and learn how much geometry has grown over time, and how people from Egypt, Greece, and France have contributed to the geometry we now use today.

Geometry is not just a math topic created to make your life harder. It is a topic that was developed to answer questions about shapes and space related to construction and surveying. It answers questions about all the different shapes we see, such as how much space an object or shape can hold. Geometry even has application in the field of astronomy, as it is used to calculate the position of stars and planets. Over time, different people contributed new and different things to grow geometry from its basic beginnings to the geometry we know, use and study today.

The first written record that we have of geometry comes from Egypt back in 2000 BC. Some of the earliest texts that have been discovered include the Egyptian Rhind papyrus, Moscow papyrus and some Babylonian clay tablets, such as the Plimpton 322. These early geometry works included formulas for calculating lengths, areas and volumes of various shapes, including those of a pyramid.

The Greeks also contributed much to the study of geometry. **Thales of Miletus**, although a Greek, actually calculated the height of pyramids in the 7th century BC. The Greek mathematician Pythagoras is well-known, and you will hear and learn much about what he contributed to the study of geometry. Also in the 7th century BC, Pythagoras is credited with proving the Pythagorean Theorem, which we currently use today when working with triangles. The Pythagorean Theorem shows that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Another Greek mathematician, **Euclid**, introduced Euclidean geometry around 300 BC. Euclidean geometry is based on a collection of basic truths and definitions presented in the 13 books written by Euclid, known as Euclid's Elements. Euclid used these basic truths and definitions in proving other theorems, such as the one that says that if two triangles have two equal sides and the angle in between the two sides is equal, then the two triangles are congruent. We still use Euclid's method of proving theorems with the use of definitions today.

The French mathematician **Rene Descartes** made a huge contribution to the study of geometry when he developed the Cartesian coordinate system in the early 17th century CE. This is the coordinate system still in use today. We use this system today to combine algebra with geometry to make it easier to notate formulas, make calculations and to draw shapes on a Cartesian graph. Descartes work in geometry also provided a basis for calculus.

We've learned that geometry is the study of shapes and space. It answers questions about size, area, and volume. The earliest known geometry works come from Egypt dating back to 2000 BC. These included formulas for lengths, areas and volumes, even one for pyramids. In the 7th century BC, Thales of Miletus calculated the height of pyramids, and the Greek mathematician Pythagoras proved the well-known Pythagorean Theorem.

Around 300 BC, Euclid, another Greek mathematician, introduced Euclidean geometry by showing how to prove theorems with the use of basic definitions and truths. Euclidean geometry is something we still use today to prove theorems. In the 17th century CE, a French mathematician named Rene Descartes developed the Cartesian coordinate system, which is still in use today. We use this system to combine algebra with geometry to make it easier to notate formulas, make calculations and draw shapes on the Cartesian graph.

After watching this lesson, you should be able to examine how people from Egypt, France, and Greece contributed to the development of geometry as we know it today.

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Geometry: High School15 chapters | 160 lessons

- What is Geometry? 4:36
- Thales & Pythagoras: Early Contributions to Geometry 5:14
- The Axiomatic System: Definition & Properties 5:17
- Euclid's Axiomatic Geometry: Developments & Postulates 5:58
- Undefined Terms of Geometry: Concepts & Significance 5:23
- Properties and Postulates of Geometric Figures 4:53
- Algebraic Laws and Geometric Postulates 5:37
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