Part of the Series: The Power of Mathematical Visualization

Inspired by a question about the Fibonacci numbers, probe the power of graphs. First, experiment with scatter plots. Then see how plotting data is like graphing functions in algebra. Use graphs to prove the fixed-point theorem and answer the Fibonacci question that opened the lecture.

Running Time

31 mins

Year

2016

Kanopy ID

2681817

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Visualizing the Fibonacci Numbers

Learn how a rabbit-breeding question in the 13th century led to the celebrated Fibonacci numbers. Investigate the properties of this sequence by focusing on the single picture that explains it all. Then hear the world premiere of Professor Tanton's amazing Fibonacci theorem!

Visualizing Balance Points in Statistics

Venture into statistics to see how Archimedes' law of the lever lets you calculate data averages on a scatter plot. Also discover how to use the method of least squares to find the line of best fit on a graph.

Symmetry: Revitalizing Quadratics Graphing

Throw away the quadratic formula you learned in algebra class. Instead, use the power of symmetry to graph quadratic functions with surprising ease. Try a succession of increasingly scary-looking quadratic problems. Then see something totally magical not to be found in textbooks.

Functions and Graphs

The 8 videos in this collection focus on all aspects of Functions and Graphs.

Linear Equations and Their Graphs

Key concepts explained: linear equations and their graphs, and the domain of an equation.

Visualizing Pascal's Triangle

Keep playing with the approach from the previous lecture, applying it to algebra problems, counting paths in a grid, and Pascal's triangle. Then explore some of the beautiful patterns in Pascal's triangle, including its connection to the powers of eleven and the binomial theorem.

Visualizing Fixed Points

One sheet of paper lying directly atop another has all its points aligned with the bottom sheet. But what if the top sheet is crumpled? Do any of its points still lie directly over the corresponding point on the bottom sheet? See a marvelous visual proof of this fixed-point theorem.

Algebra

The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions.

Trigonometry

The 11 videos in this collection focus on all aspects of Trigonometry, from Pythagoras' theorem to cosec, sec and cot.

Factoring is Fantastic

Key concepts explained: Factoring, terms, expressions, finding the greatest common factor(s), and factoring polynomial expressions that are the sums or differences of terms with common factors.
This starts with a review of numerical factors and greatest common factors, and
moves into the realm of algebra. Different types of factoring and…

Visualizing Negative Numbers

Negative numbers are often confusing, especially negative parenthetical expressions in algebra problems. Discover a simple visual model that makes it easy to keep track of what's negative and what's not, allowing you to tackle long strings of negatives and positives--with parentheses galore.

Pushing Long Division to New Heights

Put your dots-and-boxes machine to work solving long-division problems, making them easy while shedding light on the rationale behind the confusing long-division algorithm taught in school. Then watch how the machine quickly handles scary-looking division problems in polynomial algebra.

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