In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. The oldest known multiplication tables were used by the Babylonians about 4000 years ago. They used base 60. The oldest known tables using base 10 are the decimal multiplication table on bamboo strips dating to about 305 BC, found in China. The table is sometimes attributed to Pythagoras. It is also called the Table of Pythagoras in many languages (for example French, Italian and apparently Russian long ago), sometimes in English. In 493 A.D., Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144". In his 1820 book The Philosophy of Arithmetic, mathematician John Leslie published a multiplication table up to 99 × 99, which allows numbers to be multiplied in pairs of digits at a time. Leslie also recommended that young pupils memorize the multiplication table up to 25 × 25. The illustration below shows a table up to 15 × 15.
You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.
For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory. Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire.
Below is a program that was done by Nova on PBS. It was aired October 28, 2008.
Aired October 28, 2008 on PBS's Nova
This started as a way to express the admins' love of calculus and math in general. As result, this has turned into a gathering place for math-based humor and weekly challenges.
This work by Calculus Humor is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.