Complex Numbers in Geometry
Episode 35 of Geometry

The Great Courses
Show More

If you are a student or a professor:

Watch now

If you are a librarian or a professor:

Related videos

Distance, Midpoints, and Folding Ties
Episode 6 of Geometry
Learn how watching a fly on his ceiling inspired the mathematician Rene Descartes to link geometry and algebra. Find out how this powerful connection allows us to use algebra to calculate distances, midpoints, and more.
The Geometry of Figurate Numbers
Episode 34 of Geometry
Ponder another surprising appearance of geometry--the mathematics of numbers and number theory. Look into the properties of square and triangular numbers, and use geometry to do some fancy arithmetic without a calculator.
The Equation of a Circle
Episode 20 of Geometry
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.
Proofs and Proof Writing
Episode 8 of Geometry
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 Pythagorean Theorem
Episode 5 of Geometry
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.
Beginningsā€”Jargon and Undefined Terms
Episode 2 of Geometry
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 Joy of the Imaginary NumberĀ i
Episode 14 of The Joy of Mathematics
Could the apparently nonsensical number the square root of -1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear.
Memorizing Numbers
Episode 9 of Secrets of Mental Math
Think that memorizing long numbers sounds impossible? Think again. Investigate a fun: and effective: way to memorize numbers using a phonetic code in which every digit is given a consonant sound. Then practice your knowledge by trying to memorize the first 24 digits of pi, all of your credit card…
Divide and Conquer
Episode 4 of Secrets of Mental Math
Turn now to the last fundamental operation of arithmetic: division. Explore a variety of shortcuts for dividing by one- and two-digit numbers; learn how to convert fractions such as 1/7 and 3/16 into decimals; and discover methods for determining when a large number is divisible by numbers such as 3,…
Mental Addition and Subtraction
Episode 2 of Secrets of Mental Math
Professor Benjamin demonstrates how easily you can mentally add and subtract one-, two-, and three-digit numbers. He also shows you shortcuts using the complement of a number (its distance from 100 or 1000) and demonstrates the uses of mental addition and subtraction for quickly counting calories and making change.
Making Use of Linear Equations
Episode 11 of Geometry
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.
Geometry - An Interactive Journey to Mastery
Inscribed over the entrance of Plato's Academy were the words, "Let no one ignorant of geometry enter my doors." To ancient scholars, geometry was the gateway to knowledge. Its core skills of logic and reasoning are essential to success in school, work, and many other aspects of life. Yet sometimes…