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## Episodes

- S1 E1 - Geometry - Ancient Ropes and Modern PhonesMay 1, 201433minExplore the origins of one of the oldest branches of mathematics. See how geometry not only deals with practical concerns such as mapping, navigation, architecture, and engineering, but also offers an intellectual journey in its own right - inviting big, deep questions. #Science & MathematicsFree trial of The Great Courses Signature Collection or buy
- S1 E2 - Beginnings - Jargon and Undefined TermsMay 1, 201428minLay the basic building blocks of geometry by examining what we mean by the terms point, line, angle, plane, straight, and flat. Then learn the postulates or axioms for how those building blocks interact. Finally, work through your first proof - the vertical angle theorem.Free trial of The Great Courses Signature Collection or buy
- S1 E3 - Angles and Pencil-Turning MysteriesMay 1, 201428minUsing nothing more than an ordinary pencil, see how three angles in a triangle can add up to 180 degrees. Then compare how the experience of turning a pencil on a flat triangle differs from walking in a triangular shape on the surface of a sphere. With this exercise, Professor Tanton introduces you to the difference between flat and spherical geometry.Free trial of The Great Courses Signature Collection or buy
- S1 E4 - Understanding PolygonsMay 1, 201431minShapes with straight lines (called polygons) are all around you, from the pattern on your bathroom floor to the structure of everyday objects. But although we may have an intuitive understanding of what these shapes are, how do we define them mathematically? What are their properties? Find out the answers to these questions and more.Free trial of The Great Courses Signature Collection or buy
- S1 E5 - The Pythagorean TheoremMay 1, 201429minWe commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it's a critical foundation for the rest of geometry.Free trial of The Great Courses Signature Collection or buy
- S1 E6 - Distance, Midpoints, and Folding TiesMay 1, 201429minLearn how watching a fly on his ceiling inspired the mathematician René Descartes to link geometry and algebra. Find out how this powerful connection allows us to use algebra to calculate distances, midpoints, and more.Free trial of The Great Courses Signature Collection or buy
- S1 E7 - The Nature of ParallelismMay 1, 201435minExamine how our usual definition of parallelism is impossible to check. Use the fundamental assumptions from the previous lectures to follow in Euclid's footsteps and create an alternative way of checking if lines are parallel. See how, using this result, it's possible to compute the circumference of the Earth just by using shadows!Free trial of The Great Courses Signature Collection or buy
- S1 E8 - Proofs and Proof WritingMay 1, 201429minThe beauty of geometry is that each result logically builds on the others. Mathematicians demonstrate this chain of deduction using proofs. Learn this step-by-step process of logic and see how to construct your own proofs.Free trial of The Great Courses Signature Collection or buy
- S1 E9 - Similarity and CongruenceMay 1, 201434minDefine what it means for polygons to be "similar" or "congruent" by thinking about photocopies. Then use that to prove the third key assumption of geometry - the side-angle-side postulate - which lets you verify when triangles are similar. Thales of Ionia used this principle in 600 B.C.E. to impress the Egyptians by calculating the height of the pyramids.Free trial of The Great Courses Signature Collection or buy
- S1 E10 - Practical Applications of SimilarityMay 1, 201431minBuild on the side-angle-side postulate and derive other ways of testing whether triangles are similar or congruent. Also dive into several practical applications, including a trick botanists use for estimating the heights of trees and a way to measure the width of a river using only a baseball cap.Free trial of The Great Courses Signature Collection or buy
- S1 E11 - Making Use of Linear EquationsMay 1, 201429minDelve deeper into the connections between algebra and geometry by looking at lines and their equations. Use the three basic assumptions from previous lectures to prove that parallel lines have the same slope and to calculate the shortest distance between a point and a line.Free trial of The Great Courses Signature Collection or buy
- S1 E12 - Equidistance - A Focus on DistanceMay 1, 201433minYou've learned how to find the midpoint between two points. But what if you have three points? Or four points? Explore the concept of equidistance and how it reveals even more about the properties of triangles and other shapes.Free trial of The Great Courses Signature Collection or buy
- S1 E13 - A Return to ParallelismMay 1, 201431minContinue your study of parallelism by exploring the properties of transversals (lines that intersect two other lines). Prove how corresponding angles are congruent, and see how this fact ties into a particular type of polygon: trapezoids.Free trial of The Great Courses Signature Collection or buy
- S1 E14 - Exploring Special QuadrilateralsMay 1, 201430minClassify all different types of four-sided polygons (called quadrilaterals) and learn the surprising characteristics about the diagonals and interior angles of rectangles, rhombuses, trapezoids, and more. Also see how real-life objects - like ironing boards - exhibit these geometric characteristics.Free trial of The Great Courses Signature Collection or buy
- S1 E15 - The Classification of TrianglesMay 1, 201430minContinue the work of classification with triangles. Find out what mathematicians mean when they use words like scalene, isosceles, equilateral, acute, right, and obtuse. Then, learn how to use the Pythagorean theorem to determine the type of triangle (even if you don't know the measurements of the angles).Free trial of The Great Courses Signature Collection or buy
- S1 E16 - Circle-ometry - On Circular MotionMay 1, 201432minHow can you figure out the "height" of the sun in the sky without being able to measure it directly with a ruler? Follow the path of ancient Indian scholars to answer this question using "angle of elevation" and a branch of geometry called trigonometry. You learn the basic trig identities (sine, cosine, and tangent) and how physicists use them to describe circular motion.Free trial of The Great Courses Signature Collection or buy
- S1 E17 - Trigonometry through Right TrianglesMay 1, 201428minThe trig identities you explored in the last lecture go beyond circles. Learn how to define all of them just using triangles (expressed in the famous acronym SOHCAHTOA). Then, uncover how trigonometry is practically applied by architects and engineers to measure the heights of buildings.Free trial of The Great Courses Signature Collection or buy
- S1 E18 - What Is the Sine of 1°?May 1, 201432minSo far, you've seen how to calculate the sine, cosine, and tangents of basic angles (0°, 30°, 45°, 60°, and 90°). What about calculating them for other angles - without a calculator? You'll use the Pythagorean theorem to come up with formulas for sums and differences of the trig identities, which then allow you to calculate them for other angles.Free trial of The Great Courses Signature Collection or buy
- S1 E19 - The Geometry of a CircleMay 1, 201429minExplore the world of circles! Learn the definition of a circle as well as what mathematicians mean when they say things like radius, chord, diameter, secant, tangent, and arc. See how these interact, and use that knowledge to prove the inscribed angle theorem and Thales' theorem.Free trial of The Great Courses Signature Collection or buy
- S1 E20 - The Equation of a CircleMay 1, 201433minIn your study of lines, you used the combination of geometry and algebra to determine all kinds of interesting properties and characteristics. Now, you'll do the same for circles, including deriving the algebraic equation for a circle.Free trial of The Great Courses Signature Collection or buy
- S1 E21 - Understanding AreaMay 1, 201428minWhat do we mean when we say "area"? Explore how its definition isn't quite so straightforward. Then, work out the formula for the area of a triangle and see how to use that formula to derive the area of any other polygon.Free trial of The Great Courses Signature Collection or buy
- S1 E22 - Explorations with PiMay 1, 201431minWe say that pi is 3.14159 ... but what is pi really? Why does it matter? And what does it have to do with the area of a circle? Explore the answer to these questions and more - including how to define pi for shapes other than circles (such as squares).Free trial of The Great Courses Signature Collection or buy
- S1 E23 - Three-Dimensional Geometry - SolidsMay 1, 201432minSo far, you've figured out all kinds of fun properties with two-dimensional shapes. But what if you go up to three dimensions? In this lecture, you classify common 3-D shapes such as cones and cylinders, and learn some surprising definitions. Finally, you study the properties (like volume) of these shapes.Free trial of The Great Courses Signature Collection or buy
- S1 E24 - Introduction to ScaleMay 1, 201430minIf you double the side-lengths of a shape, what happens to its area? If the shape is three-dimensional, what happens to its volume? In this lecture, you explore the concept of scale. You use this idea to re-derive one of our fundamental assumptions of geometry, the Pythagorean theorem, using the areas of any shape drawn on the edges of the right triangle - not just squares.Free trial of The Great Courses Signature Collection or buy
- S1 E25 - Playing with Geometric ProbabilityMay 1, 201430minUnite geometry with the world of probability theory. See how connecting these seemingly unrelated fields offers new ways of solving questions of probability - including figuring out the likelihood of having a short wait for the bus at the bus stop.Free trial of The Great Courses Signature Collection or buy

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## Details

### More info

- Audio languages
- English

- Subtitles
- English [CC]

- Producers
- The Great Courses

- Cast
- James Tanton

- Studio
- The Great Courses

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