

Geometry: An Interactive Journey to Mastery
The Great Courses Signature Collectionの無料体験または購入
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エピソード
シーズン1エピソード1 - Geometry - Ancient Ropes and Modern Phones
2014年5月1日33分Explore 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 & MathematicsThe Great Courses Signature Collectionの無料体験または購入シーズン1エピソード2 - Beginnings - Jargon and Undefined Terms
2014年5月1日28分Lay 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード3 - Angles and Pencil-Turning Mysteries
2014年5月1日28分Using 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード4 - Understanding Polygons
2014年5月1日31分Shapes 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード5 - The Pythagorean Theorem
2014年5月1日29分We 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード6 - Distance, Midpoints, and Folding Ties
2014年5月1日29分Learn 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード7 - The Nature of Parallelism
2014年5月1日35分Examine 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!The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード8 - Proofs and Proof Writing
2014年5月1日29分The 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード9 - Similarity and Congruence
2014年5月1日34分Define 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード10 - Practical Applications of Similarity
2014年5月1日31分Build 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード11 - Making Use of Linear Equations
2014年5月1日29分Delve 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード12 - Equidistance - A Focus on Distance
2014年5月1日33分You'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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード13 - A Return to Parallelism
2014年5月1日31分Continue 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード14 - Exploring Special Quadrilaterals
2014年5月1日30分Classify 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード15 - The Classification of Triangles
2014年5月1日30分Continue 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).The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード16 - Circle-ometry - On Circular Motion
2014年5月1日32分How 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード17 - Trigonometry through Right Triangles
2014年5月1日28分The 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード18 - What Is the Sine of 1°?
2014年5月1日32分So 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード19 - The Geometry of a Circle
2014年5月1日29分Explore 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード20 - The Equation of a Circle
2014年5月1日33分In 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード21 - Understanding Area
2014年5月1日28分What 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード22 - Explorations with Pi
2014年5月1日31分We 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).The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード23 - Three-Dimensional Geometry - Solids
2014年5月1日32分So 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード24 - Introduction to Scale
2014年5月1日30分If 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.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード25 - Playing with Geometric Probability
2014年5月1日30分Unite 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.The Great Courses Signature Collectionの無料体験または購入