Bringing Visual Mathematics Together

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The Figure: Drawing Projects
Episode 34 of How to Draw
Finish exploring human anatomy, covering the muscles of the lower body and limbs. Then bring your knowledge to a spectrum of drawing projects, beginning with a full-length self-portrait in three views. Draw variations such as figures in one- and two-point perspective, a figure within an invented room, and figures in…
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.
Visualizing Orderly Movement, Random Effect
Start with a simulation called Langton's ant, which follows simple rules that produce seemingly chaotic results. Then watch how repeated folds in a strip of paper lead to the famous dragon fractal. Also ask how many times you must fold a strip of paper for its width to equal the…
Proportion: Accurate Proportion and Measure
Episode 12 of How to Draw
Study key tools artists use to arrive at correct proportions. In particular, learn how to use an analog clock face as a way to quantify angles, how to use a standard unit of measure to measure across the picture plane, and how to use level and plumb lines. Then put…
Advanced Drawing Projects
Episode 36 of How to Draw
Conclude with challenging projects that weave together observation and imagination, as well as abstraction and representation. Explore how to develop subject matter and source material for your drawings. Locate areas of personal interest, themes, and ideas to identify the kind of art you want to make and cultivate your own…
Drawing Fundamentals and First Exercises
Episode 3 of How to Draw
Explore essential first drawing exercises and learn how you will apply the skills developed here to much more complex subjects. Grasp how the curriculum--spanning the many pieces making up the "grammar" of drawing, such as composition, proportion, perspective, value, texture, and color--fits together, providing you with the knowledge and ability…
When an Essayist’s Feelings Face Facts
To help keep your essays from becoming overly sentimental, Professor Cognard-Black discusses pitfalls for writers to avoid. You'll be introduced to three examples of what rhetorical theorists call logical fallacies and then take on the challenge of an assignment that brings together emotional appeals with rational ones to achieve credibility,…
The T Word Theme (A-list Screenwriting Series)
Part of the Series: A-list Screenwriting Series
As Hollywood uses the term, "story" is only one element of a great screenplay. Writers who have something to say about the world must learn how film and drama convey theme and ideas. Great writers seem to understand theme intuitively. They are able to achieve thematic clarity without being didactic.…
The Power of a Mathematical Picture
Professor Tanton reminisces about his childhood home, where the pattern on the ceiling tiles inspired his career in mathematics. He unlocks the mystery of those tiles, demonstrating the power of visual thinking. Then he shows how similar patterns hold the key to astounding feats of mental calculation.
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.
Visualizing Ratio Word Problems
Word problems. Does that phrase strike fear into your heart? Relax with Professor Tanton's tips on cutting through the confusing details about groups and objects, particularly when ratios and proportions are involved. Your handy visual devices include blocks, paper strips, and poker chips.
Visualizing Extraordinary Ways to Multiply
Consider the oddity of the long-multiplication algorithm most of us learned in school. Discover a completely new way to multiply that is graphical--and just as strange! Then analyze how these two systems work. Finally, solve the mystery of why negative times negative is always positive.