James S Tanton
Author
Series
Language
English
Description
Learn why quadratic equations have "quad" in their name, even though they don't involve anything to the 4th power. Then try increasingly challenging examples, finding the solutions by sketching a square. Finally, derive the quadratic formula, which you've been using all along without realizing it.
Author
Series
Great Courses volume 24
Language
English
Description
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.
Author
Series
Great Courses volume 15
Language
English
Description
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).
Author
Series
Great Courses volume 10
Language
English
Description
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.
Author
Series
Great Courses volume 28
Language
English
Description
You've seen geometric tiling patterns on your bathroom floor and in the works of great artists. But what would happen if you made repeating patterns in 3-D space? In this lecture, discover the five platonic solids! Also, become an artist and create your own beautiful patterns - even using more than one type of shape.
Author
Series
Great Courses volume 4
Language
English
Description
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.
Author
Series
Great Courses volume 30
Language
English
Description
Human aesthetics seem to be drawn to symmetry. Explore this idea mathematically through the study of mappings, translations, dilations, and rotations - and see how symmetry is applied in modern-day examples such as cell phones.
Author
Series
Great Courses volume 13
Language
English
Description
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.
Author
Series
Great Courses volume 17
Language
English
Description
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.
Author
Series
Great Courses volume 32
Language
English
Description
If you have a fixed-length string, what shape can you create with that string to give you the biggest area? Uncover the answer to this question using the legendary story of Dido and the founding of the city of Carthage.
Author
Series
Great Courses volume 29
Language
English
Description
Use paper-folding to unveil sets of curves: parabolas, ellipses, and hyperbolas. Study their special properties and see how these curves have applications across physics, astronomy, and mechanical engineering.
Author
Series
Great Courses volume 9
Language
English
Description
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.
Author
Series
Great Courses volume 35
Language
English
Description
In lecture 6, you saw how 17th-century mathematician René Descartes united geometry and algebra with the invention of the coordinate plane. Now go a step further and explore the power and surprises that come from using the complex number plane. Examine how using complex numbers can help solve several tricky geometry problems.
Author
Series
Great Courses volume 21
Language
English
Description
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.
Author
Series
Great Courses volume 36
Language
English
Description
Wrap up the course by looking at several fun and different ways of reimagining geometry. Explore the counterintuitive behaviors of shapes, angles, and lines in spherical geometry, hyperbolic geometry, finite geometry, and even taxi-cab geometry. See how the world of geometry is never a closed-book experience.
Author
Series
Great Courses volume 33
Language
English
Description
Wander through the crazy, counterintuitive world of rotations. Use a teacup and string to explore how the mathematics of geometry can describe an interesting result in quantum mechanics.
Author
Series
Great Courses volume 12
Language
English
Description
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.
Author
Series
Great Courses volume 23
Language
English
Description
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.
Author
Series
Great Courses volume 31
Language
English
Description
Explore the beautiful and mysterious world of fractals. Learn what they are and how to create them. Examine famous examples such as Sierpinski's Triangle and the Koch Snowflake. Then, uncover how fractals appear in nature - from the structure of sea sponges to the walls of our small intestines.
Author
Series
Great Courses volume 3
Language
English
Description
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.