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.
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The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods.
In this applet, polygons are inscribed and circumscribed around circles. The area of the polygons around a circle of radius 1 are calculated on the left, and the perimeter of the polygons around a circle of diameter 1 are calculated on the right. Change the value of n to increase or decrease the number of sides in the polygons, and notice how the calculations of the areas and perimeters begin to approximate pi.
The inscribed polygon is blue, and the circumscribed polygon is red. Not surprisingly, the blue polygon gives an underestimate, and the red polygon gives an overestimate. But by how much?
This is an activity from Illuminations which is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.
** WE DO NOT OWN THIS. WE ARE ONLY SHARING! **** "Funny Little Calculus Text" is owned by Robert Ghrist at the University of Pennsylvania **
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.
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