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.

Geoffrey of Monmouth’s History of the Kings of Britain is arguably the most important literary artifact of the Arthurian tradition. Learn about the political nature of the text, the important elements and characters that Geoffrey wove into it, and how he established the basics of the Arthurian legend as we know it..

Discover the rich world of adverbs, as they modify not only verbs, but also adjectives, other adverbs, clauses, and sentences. Investigate intensifiers (such as very," "surely," and "possibly"), which can either strengthen or hedge statements, and study the subtleties of "flat" adverbs-adverbs that have the same form as their adjective counterparts."

Learn about Maya life through their art, studying such works as the fantastic painted murals at Bonampak and the famous sarcophagus lid on the tomb of Pakal. According to a best-selling book, the latter depicts an ancient astronaut on a rocket ship, but Dr. Barnhart decodes its real meaning.

While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson's paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine, where it can lead to inappropriate treatments.

In the 1880s, Albert Michelson and Edward Morley conducted an experiment to determine the motion of Earth relative to the ether. You'll learn about their experiment, its shocking result, and the resulting theoretical crisis.

Look now at events surrounding Jesus's death that we cannot know about with certainty. Assess the plausibility of the Gospels' accounts of his arrival in Jerusalem, the date of his crucifixion, and the matter of his burial. Grasp how Christian writers made changes in the accounts of his death to serve theological ends.

Music is an integral part of humanity. Every culture has music, from the largest society to the smallest tribe. Its marvelous range of melodies, themes, and rhythms taps into something universal. Babies are soothed by it. Young adults dance for hours to it. Older adults can relive their youth with the vivid memories it evokes. Music is part of our most important rituals, and it has been the medium of some of our greatest works of art. Yet even though...

Turn your attention to versatile, inexpensive root vegetables with this lesson on how to select, store, and cook carrots, celery root, and parsnips. Watch as Chef Briwa prepares crudités with tapenade; parsnip chips; celery root tonkatsu with rice and napa cabbage salad; and carrot cake with a parsnip-infused icing.

Delve into Bertrand Russell's profoundly simple paradox that undermined Cantor's theory of sets. Then follow the scramble to fix set theory and all of mathematics with a new set of axioms, designed to avoid all paradoxes and keep mathematics consistent - a goal that was partly met by the Zermelo-Fraenkel set theory.