Geometry: An Interactive Journey to Mastery
Where to Watch Geometry: An Interactive Journey to Mastery
36.
Bending the Axioms - New Geometries
2014-05-02
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.
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35.
Complex Numbers in Geometry
2014-05-02
In lecture 6, you saw how 17th-century mathematician Rene 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.
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34.
The Geometry of Figurate Numbers
2014-05-02
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.
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33.
The Geometry of Braids - Curious Applications
2014-05-02
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.
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32.
Dido's Problem
2014-05-02
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.
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31.
The Mathematics of Fractals
2014-05-02
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.
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30.
The Mathematics of Symmetry
2014-05-02
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.
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29.
Folding and Conics
2014-05-02
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.
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28.
Tilings, Platonic Solids, and Theorems
2014-05-02
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?
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27.
The Reflection Principle
2014-05-02
If you're playing squash and hit the ball against the wall, at what angle will it bounce back? If you're playing pool and want to play a trick shot against the side edge, how do you need to hit the ball?
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26.
Exploring Geometric Constructions
2014-05-02
Let's say you don't have a marked ruler to measure lengths or a protractor to measure angles. Can you still draw the basic geometric shapes?
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25.
Playing with Geometric Probability
2014-05-02
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.
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24.
Introduction to Scale
2014-05-02
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?
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23.
Three-Dimensional Geometry - Solids
2014-05-02
So far, you've figured out all kinds of fun properties with two-dimensional shapes. But what if you go up to three dimensions?
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22.
Explorations with Pi
2014-05-02
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).
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21.
Understanding Area
2014-05-02
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.
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20.
The Equation of a Circle
2014-05-02
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.
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19.
The Geometry of a Circle
2014-05-02
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.
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18.
What Is the Sine of 1°?
2014-05-02
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?
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17.
Trigonometry through Right Triangles
2014-05-02
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).
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16.
Circle-ometry - On Circular Motion
2014-05-02
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.
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15.
The Classification of Triangles
2014-05-02
Continue the work of classification with triangles. Find out what mathematicians mean when they use words like scalene, isosceles, equilateral, acute, right, and obtuse.
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14.
Exploring Special Quadrilaterals
2014-05-02
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.
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13.
A Return to Parallelism
2014-05-02
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.
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12.
Equidistance - A Focus on Distance
2014-05-02
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.
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11.
Making Use of Linear Equations
2014-05-02
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.
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10.
Practical Applications of Similarity
2014-05-02
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.
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9.
Similarity and Congruence
2014-05-02
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.
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8.
Proofs and Proof Writing
2014-05-02
The beauty of geometry is that each result logically builds on the others. Mathematicians demonstrate this chain of deduction using proofs.
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7.
The Nature of Parallelism
2014-05-02
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.
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6.
Distance, Midpoints, and Folding Ties
2014-05-02
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.
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5.
The Pythagorean Theorem
2014-05-02
We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that.
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4.
Understanding Polygons
2014-05-02
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?
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3.
Angles and Pencil-Turning Mysteries
2014-05-02
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.
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2.
Beginnings - Jargon and Undefined Terms
2014-05-02
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.
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1.
1. Geometry - Ancient Ropes and Modern Phones
2014-05-01
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.
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Geometry: An Interactive Journey to Mastery is a series categorized as a cancelled. Spanning 1 seasons with a total of 36 episodes, the show debuted on 2014. The series has earned a no reviews from both critics and viewers. The IMDb score stands at undefined.
How to Watch Geometry: An Interactive Journey to Mastery
How can I watch Geometry: An Interactive Journey to Mastery online? Geometry: An Interactive Journey to Mastery is available on The Great Courses with seasons and full episodes. You can also watch Geometry: An Interactive Journey to Mastery on demand at Prime Video, Apple TV Channels, Amazon online.
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