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Thursday, March 14, 2013
Happy π Day! Pi has been known to most cultures since antiquity, with the earliest known calculations dating back to the Great Pyramid at Giza, whose perimeter measures about 1760 cubits and a height of about 280 cubits, giving the ratio 1760/280 ≈ 6.2857 which is approximately equal to 2π ≈ 6.2832. The earliest verifiable use of the lower case Ancient Greek letter π (pi) to symbolize the ratio of the diameter of a circle to its circumference was by the mathematician William Jones in his 1706 work a New Introduction to the Mathematics. In that work, however, Jones says that the ‘truly ingenious Mr. John Machin’ used it before him. There are many ways to derive π (pi), from the rough approximation of 22/7 to the most recent calculations that extend π (pi) to over a trillion digits, calculated over months and years with supercomputers.
Apologies to all those not in the Eastern Time zone of the United States-this post should hit your dashboard on 3/14 at 1:59.
Calling all Etymologers! Kidsneedscience is looking for talented writers with an interest in word histories and science, technology, engineering and math. Are you fascinated by science and discovery and love how their discoveries and innovations translate into words and culture? Are you secretly thrilled to find connections between words you never knew existed? Consider submitting a sample post-kidsneedscience is looking for contributors to grow this website. Right now KNS has over 60,000 followers and is growing. Are you studying molecular biology and want to write about interesting words? Did you take Latin or Greek in school and wouldn’t mind finding your dictionaries and lexicons on your bookshelf? Submit a sample post to me via direct message. Posts can be anywhere from 100-400 words and tell a compelling story about a word or name from science or math. Students and educators welcome.
Style guide is short and simple: third person voice, key word in bold, root words and definitions in italic. If you have rights to a photo or illustration for your word, perfect! If not we will find one.
Image courtesy the Oxford Universal English Dictionary, published 1937. Full details here.
The word bifurcation entered modern usage courtesy of the French mathematician Jules Henri Poincare with the publication of his work, L’Équilibre d’une masse fluide animée d’un mouvement de rotation, as part of the Acta Mathematica, and first appeared in September 1885. Poincare is known as the last true great universalist in mathematics-he was skilled in most areas of math and is known today for his formulation of what was kown for a century as the Poincare Conjecture before it was solved in 2005. Poincare coined the word bifurcation to describe the divergence of two states from a common smooth state: a bifurcation occurs when a small change made to the parameter values of a system causes a sudden qualitative or topological change in its behaviour.
The word bifurcation comes directly from the Latin word furca meaning fork, attaching the prefix bi- meaning two. It should be noted that the word furca also had metaphorical and figurative uses in Roman times and the Romans had the word tridens (corresponding directly to the English word trident) which looked more like a modern fork than the two pronged affair used by Romans. In defense of Poincare, he was seeking a strict mathematical definition-he needed to limit the sense to two options as a starting point-he wanted to be sure that the furca imagined was limited to two options and not three.
Image of Poincare in the public domain. Image of Roman fork of unknown provenance.
Science is a process of collaboration that often happens over hundreds of years and across many countries and combines the talents of hundreds and thousands of people. Some scientists have more influence than others, whether or not they are recognized for it. Today is the birthday of Gaspard Bauhin, born in Basel Switzerland on 17 January 1560 (died 5 December 1624), who is in many ways responsible for introducing the practice of using binomial names to denote species and genus. Bauhin was a multi-talented polymath with degrees as a doctor who also taught Ancient Greek.
The word binomial entered English in the 1550s from the Late Latin word binomius meaning two personal names, itself a combination of the Latin prefix bi- meaning two and nomen meaning name. It was used in the 16th century in algebra to denote an expression with two terms. It wasn’t until Linneaus popularized the work of Bauhin that the binomial was commonly used in taxonomy.
A torus is shape defined as the shape formed by rotating a circle around an axis coplanar with the circle. The resulting shape will have one of three forms: a ring torus, in which the axis of revolution does not touch the circle; a horn torus, in which the circle is tangent to the axis; and a spindle torus, in which the axis is a chord of the circle. There are many real examples of the torus shape around the house: donuts, bundt cakes, life preservers, bicycle inner tubes and cushions.
The word torus is unchanged from Ancient Rome: the Latin word torus was a cushion. In architecture, the base of many columns contains a toroid, which acts as a ‘cushion’ for the column.
GIF of torus shapes courtesy Kieff who created the GIF and released it to the public domain. Thank you Kieff for such a beautiful image, and thank you for sharing your work with the world!
Image of The Column of Trajan, Rome, Dedicated in A.D. 113 to commemorate the emperor’s victory over the Dacians courtesy Roger Ulrich under a Creative Commons 3.0 license. Thank you Roger for releasing your word to Creative Commons.
When the Egyptian demi-god and Pharaoh Ptolemy I Soter asked his tutor Euclid of Alexandria if there was an easier way to learn geometry, Euclid is said to have replied that there was no royal road to knowledge. While this story is almost certainly apocryphal and not written down for almost 700 years by Proclus in the 4th century AD, there is wisdom in what Euclid was reported to have said. His Elements stands as the first comprehensive mathematical work, a giant work that continues to define the basis of modern (ahem, non-Euclidean) geometry. The first main obstacle in Book 1 of the Elements is the Fifth proposition, known since antiquity in Latin as the Pons Asinorum, or in English as the ‘bridge of asses’. Perhaps Ptolemy stumbled when confronted with the difficulty of understanding the theorem of isosceles triangles. Perhaps the larger and thornier issue suggested by the Fifth postulate (note that the Fifth proposition and Fifth postulate are not the same, though both lead mathematicians to non-Euclidean geometries) gave him pause.
Today the pons asinorum is used metaphorically to mean any barrier between knowledge and how it is acquired. It also has special use in logic for the perils inherent in discovering the middle term of a syllogism as illustrated above. It has also been long suggested that the name comes from the shape of the proposition when drawn, as it resembles a bridge.
Today Euclid’s reprimand of Ptolemy still holds: do your homework!
Images, left to right: Ptolemy I Soter, a 17th century engraving of the pons asinorum in logic, and Euclid’s fifth proposition.
The word (and concept) of billion is relatively new to human thought. Sure the Ancient Greeks were predicting and naming numbers far larger than a billion, but in popular use the concepts of million and billion are relatively new to human history. A billion was just a really big number-very hard to imagine in real terms, an abstract notion that for most meant something like ‘too much to count’. Etymologically, billion is a fabrication, a 15th century combination of the prefix bi- and the word million, itself a modern word. Coming to English in the 1680s, from French mathematician Nicolas Chuquet who named a million million a byllion in his unpublished work Le Triparty en la Science des Nombres from 1484. In England and Germany numbers were compiled in groups of sixes, later altered by the French into groups of three and becoming a thousand million, which is its current US meaning. Chuquet was interested in naming huge numbers and devised the system of grouping by sixes, summarizing it this way starting with: million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go…
Carl Sagan made the notion and number both popular and accessible describing the size of the universe and the number of stars and galaxies in it. Although famous for the phrase ‘billions and billions’, it wasn’t a phrase that Sagan had used by the time he became both known and parodied for it. He later embraced it as a calling card, opening speeches and presentations with his signature ‘quote’. A billion can be visualized as a cube of marbles 1000 marbles high 1000 marbles wide and 1000 marbles deep. This cube would be approximately 40 feet to a side-and weigh many many tons.
On October 31, 2011 the world population is estimated to have reached 7 billion, adding one billion people in just 42 years.
Maria Agnesi was an Italian mathematician, linguist and philospher known as the first person to write about both differential and integral calculus. A child prodigy, she spoke Italian and French, Hebrew and German, Latin and Ancient Greek, studying literature and philosophy before devoting herself to mathematics. By the age of 30 she published her signature work, the Instituzioni analitiche ad uso della gioventù italiana, which among other topics described a formula that has been given her name. The Witch of Agnesi (pictured above) is a curve that has the following Cartesian equation:
Note that if a=1/2, then this equation becomes rather simple:
The history of the name is what is unusual. Maria Agnesi was nothing if not the most accomplished woman of her day-appointed by Pope Benedict XIV to the faculty at the University of Bologna, the first woman appointed to a professorship ever.
The Instituzioni analitiche…, among other things, discussed a curve earlier studied and constructed by Pierre de Fermat and Guido Grandi. Grandi called the curve versoria in Latin and suggested the term versiera for Italian, possibly as a pun: ‘versoria’ is a nautical term , “sheet”, while versiera/aversiera is “she-devil”, “witch”, from Latin Adversarius, an alias for “devil” (Adversary of God). For whatever reasons, after translations and publications of the Instituzioni analitiche… the curve has become known as the “Witch of Agnesi”.
Video courtesy wolfram mathematica. Thanks also to wikipedia for concise history of the mis-naming of the curve.
Rene Descartes was a French mathemetician and philosopher who lived from March 1596 to February 1650. In his lifetime he revolutionized both mathematics and philosophy, and today we remember him in math with the Cartesian coordinate system. A Cartesian coordinate system is a mathematical tool for describing the relationships between any two points by locating them on a grid, simplifying and codifying their relationships. The Cartesian coordinate system is the foundation of analytic geometry and has been applied to many branches of mathematics and science.
We start with Rene Descartes today to honor an early unfinished work of his, the Rules for the Direction of the Mind. From the Rules: RULEV. Method consists entirely in the order and disposition of the objects towards which our mental vision must be directed if we would find out any truth. We shall comply with it exactly if we reduce involved and obscure propositions step by step to those that are simpler, and then starting with the intuitive apprehension of all those that are absolutely simple, attempt to ascend to the knowledge of all others by precisely similar steps.
It seems fitting on the first day of the year to follow this rule-paraphrased by most as start at the beginning and move forward-as we start the new year.
Animation of points in a Cartesian coordinate system courtesy of the Elica Team.