New Book! - Hinged Dissections: Swinging & Twisting of relationships such as the Pythagorean theorem, dissections have had a surprisingly rich history, reaching back to arabian mathematicians a millennium ago http://www.cs.purdue.edu/homes/gnf/book2.html
Extractions: by Greg Frederickson Cambridge University Press , 2002, ISBN 0-521-81192-9 (hardcover). A geometric dissection is a cutting of a geometric figure into pieces that we can rearrange to form another figure. As visual demonstrations of relationships such as the Pythagorean theorem, dissections have had a surprisingly rich history, reaching back to Arabian mathematicians a millennium ago and Greek mathematicians more than two millennia ago. As mathematical puzzles they enjoyed great popularity a century ago, in newspaper and magazine columns written by the American Sam Loyd and the Englishman Henry Ernest Dudeney. Loyd and Dudeney set as a goal the minimization of the number of pieces. Their puzzles charmed and challenged readers, especially when Dudeney introduced an intriguing variation in his 1907 book The Canterbury Puzzles . After presenting the remarkable 4-piece solution for the dissection of an equilateral triangle to a square, Dudeney wrote: I add an illustration showing the puzzle in a rather curious practical form, as it was made in polished mahogany with brass hinges for use by certain audiences. It will be seen that the four pieces form a sort of chain, and that when they are closed up in one direction they form a triangle, and when closed in the other direction they form a square. This hinged model, has captivated readers ever since. There is something irresistible about the idea of swinging hinged pieces one way to form one figure, and another way to form another figure. You do not really need a physical model to enjoy this property. Once you have examined this figure, you will be swinging mental images of the pieces around in your mind.
Ancient Egyptian Alchemy And Science its way to Europe, and arabian mathematicians, physicians, alchemists, were held in Arabian translations, elaborations and commentaries from ancient Greek and GreekEgyptian authors http://www.crystalinks.com/egyptscience.html
Extractions: The ancient Egyptians had many advanced scientific technologies, with much being found in picture form and in three-dimensional models throughout Egypt. Themes reflecting scientific knowledge and achievement can be found throughout the world in various ancient civilizations. These teachings seemed to center on electromagnetic energies. Scenes depict scientists of that timeline able to work in fields of alchemy, biology, chemistry, dentistry, anesthesiology, air flight , and the electromagnetic energies of the Great Pyramid among other sacred sites - how that link together and to the sacred geometry that forms our universe. Much of the interpretation is left to those in our timeline to decipher. Rare squared form of tet, at left. The heavy animal may be a ancient symbol for heavy electrons; the squaring may be an ancient way of referring to water. The tet might employ magneto hydrodynamic principles like ancient Egyptian and modern transportation technology, but it may employ it in obtaining energy from certain materials as well. The study of science and medicine were closely linked to religion as seen in many of the ancient rituals. The "pouring" and "anointing" we see in so many Egyptian works is the application of electromagnetic forces and not the application of actual fluids. Much of this was linked with 'magic' of some sort - as many unexplained things did occur. These were often considered miracles.
Technical Arts Related To Alchemy In Old Egypt positions as physicians, as tronomers, mathematicians, engineers, etc., and the Syrian manuscripts way to Europe, and. arabian mathematicians, physicians, alchemists, were held in http://www.levity.com/alchemy/islam07.html
Definition Of Algorism - WordIQ Dictionary & Encyclopedia arabian mathematicians made many contributions (including the concept of the decimal fractions as an extension of the notation), and the written European form http://www.wordiq.com/definition/Algorism
Extractions: Algorism is the name for the Indo-Arabic decimal system of writing and working with numbers, in which symbols (the ten digits through 9) are used to describe values using a place-value system ( positional notation ), where each symbol has ten times the weight of the one to its right. This system was originally invented in India in the 6th century AD (or earlier), and was soon adopted in the Arab world. Arabian mathematicians made many contributions (including the concept of the decimal fractions as an extension of the notation, which led to the notion of the decimal point ), and the written European forms of the digits called Arabic numerals are derived from the ghubar (sand-table or dust-table) numerals used in north-west Africa and Spain. The word algorism comes from the Arabic al-Khwarizmi algorithm Contact Us About Us
YaleGlobal Online Magazine Zero reached Baghdad by 773 AD and would be developed in the Middle East by arabian mathematicians who would base their numbers on the Indian system. http://yaleglobal.yale.edu/about/zero.jsp
CATHOLIC ENCYCLOPEDIA: Balthasar Boncompagni It is supposed to be a translation of the famous treatise on arithmetic of Alkhwarizmi, the most illustrious of the arabian mathematicians. http://www.newadvent.org/cathen/02654a.htm
Extractions: Home Encyclopedia Summa Fathers ... B > Balthasar Boncompagni A B C D ... Z Italian mathematician, b. at Rome, 10 May, 1821; d. 13 April, 1894. He was a member of the illustrious family to which had belonged Gregory XIII , the reformer of the calendar. He studied mathematics and physics under Santucci and became known as a prolific writer on mathematical and historical subjects. At an early age (1840) he contributed to the "Giornale Arcadico" biographical sketches of Father Joseph Calandrelli, director of the observatory of the Roman College after the suppression of the Society of Jesus Nuova Enciclopedia Italiana, Suppl. , 6th ed., Turin; BALL, Hist. of Mathematics (New York, 1888). H. M. BROCK
Math Lair - Arabic Math History Europe. 750 AD arabian mathematicians adopt what we now call the Arabic number system. This system was imported from India. 820 http://www.stormloader.com/ajy/arab.html
HINDU VEDANTA CULTURE AND RESEARCH to be rising in early morning. Arabian astronomers, who transmitted most of the knowledge of astronomy stars Merak and Dubhe. arabian mathematicians and astronomers had, as a well http://www.iskcon.biz/mahabarath astrnomical proof.htm
Extractions: Mahabharat: An Astronomical Proof from the Bhagavat Puraan Fortunately, many works of the Vedic and Puranic tradition contain a sufficient number of clues in the form of astronomical observations which can be used to determine the approximate date of Mahabharata and thus establish the historical authenticity of the events described in this great epic. Notable among these works are the Parashar Sanghita, the Bhagvat Puran, Shakalya Sanghita, and the Mahabharat itself. Aryabhatta, one of the greatest mathematicians and astronomers of India in the fifth century AD, examined the astronomical evidence described in the Mahabharata in his great work known as the "Aryabhattiya". According to the positions of the planets recorded in the Mahabharata, its approximate date was calculated by Aryabhatta to be 3100 BC implying that the great war described in the Mahabharata was fought approximately 5000 years ago, as most Hindus have always believed. Exhibit 1 Approximate Positions of the Saptarshis (August 1990) North . * Dubhe .
Our Non-Western Roots Of Science Algebra. Algebra ie arithmetics (basic calculating rules), disciplines of equations and series - was developed by Hindu and arabian mathematicians. http://www.cs.joensuu.fi/~whamalai/skc/prehistory.html
Extractions: We shall consider the early development of science, and especially mathematics, from the Stone Age to the Renaissance, when the golden age of our Western science begun. The emphasis is in the influence of other cultures on our scientific tradition. We know the difficulties of telling scientific truth about history, and this problem is even more crucial when describing and explaining develeopment in prehistoric times. Thus, I don't argue that the following story is truth, but just my interpretation based on general beliefs and opinions, how the human thinking and science have developed. When people (especially our ancestors, Homo sapiens; we don't know if the Neanderthal people could speak) learnt to speak ( faculty of speech ), they could transfer their knowledge and experiences to their children, and the human knowledge begun to accumulate. The knowledge was not strictly separated from beliefs, but people still wanted to give explanations for all phenomena they experienced and thought. Certainly some pieces of that "knowledge" (our common sense knowledge) would still be considered as knowledge, but more difficult things like beginning of world, origins of people and all anmals, life and death were explained by stories. They were not accepted scientific theories, but more like hypotheses, which mixed fact and fiction. Development of agriculture have usually been considered as beginning of sivilization (society and culture) with permanent settlement. It is believed that use of numbers developed already before that, with cattle-farming (about 6000 B.C. or earlier), for the purposes of counting the animals. However, the
YaleGlobal Online Magazine First, the great Arabian voyagers would bring the texts of Brahmagupta and his colleagues back from India in the Middle East by arabian mathematicians who would base their numbers http://www.yaleglobal.yale.edu/about/zero.jsp
Extractions: Week of Jan. 25, 2003; Vol. 163, No. 4 Ivars Peterson In recreational mathematics, a geometric dissection involves cutting a geometric figure into pieces that you can reassemble into another figure. For example, it's possible to slice a square into four angular pieces that can be rearranged into an equilateral triangle. The same four pieces can be assembled into a square or an equilateral triangle. Such puzzles have been around for thousands of years. The problem of dissecting two equal squares to form one larger square using four pieces dates back to at least the time of the Greek philosopher Plato (427 BC BC ). In the 10th century, Arabian mathematicians described several dissections in their commentaries on Euclid's Elements . The 18th-century Chinese scholar Tai Chen presented an elegant dissection for approximating the value of pithe ratio of a circle's circumference to its diameter. Others worked out dissection proofs of the Pythagorean theorem. In the 19th century, dissection puzzles were an immensely popular staple of magazine and newspaper columns by puzzlists San Loyd in the United States and Henry E. Dudeney in England. Dissections can get quite elaborate: A seven-pointed star becomes two heptagons; a dodecagon turns into three identical squares; and so on. You can also add constraints. For example, the pieces can be attached to one another by hinges. In the square-triangle dissection, the hinged pieces form a sort of chain. When closed in one direction, the pieces settle snugly into a square; when closed in the other direction, they fold into a triangle. (For an animated version of this dissection, see
Technical Arts Related To Alchemy In Old Egypt them transmitted to Arab scholars, found its way to Europe, and arabian mathematicians, physicians, alchemists, were held in high esteem as scientific experts. http://www.alchemywebsite.com/islam07.html
Section RT 2 of Pappus's work and for the interest that modern mathematicians found in it. can find in treatises of Diophantus, arabian mathematicians, Leonardo Fibonacci, Luca Pacioli http://www.smhct.org/Secciones RT/seccion 2.htm
Extractions: Section RT 2 Date: 9 July Classical and oriental antiquity Chair: Ivo H. L. Schneider Board: Konstantino Nikolantolakis Abstracts Participants: Date: July 9th Room: C7, Palacio de Minería Alain Bernard The Sophistic Aspects of Pappu's Mathematical Collection Gustavo Cassinelli and Guillermo Cornero Un sistema de infraestructura de transporte en el antiguo Egipto Boris A. Frolov The Ancient Evidences of the Science Genesis Shigeru Jochi The "Jiu Zhang Suan Shu" and the "Suanshushu" in 186 B. C. Greg Whitesides Reflections of the Tiangong Kaiwu: Science, Technology and Society in the Late Ming Period Alberto Jori Dalla metafisica alla fisica: l'astronomia greca nei secoli IV e III a. C. Konstantinos Nikolantonakis Serenus d' Antoine: entre Apollonios de Perge et Thabit ibn Qurra. Astrid Schuermann Aristotle on Science and Women Galina Smirnova Hero of Alexandria and Diophantine Equations Christian Velpry Euclide (1): sa logique, sa géométrie font rupture avec la tradition hellène
Mahabharat: Proof From The Bhagavat Puraan arabian mathematicians and astronomers had, as a well established fact of history, acquired most of their knowledge of algebra, arithmatic and astronomy from http://www.geocities.com/dipalsarvesh/mahabharat_astronomy1.html
Extractions: Mahabharat: An Astronomical Proof from the Bhagavat Puraan By Dr. Satya Prakash Saraswat Reproduced without permission. Fortunately, many works of the Vedic and Puranic tradition contain a sufficient number of clues in the form of astronomical observations which can be used to determine the approximate date of Mahabharata and thus establish the historical authenticity of the events described in this great epic. Notable among these works are the Parashar Sanghita, the Bhagvat Puran, Shakalya Sanghita, and the Mahabharat itself. Aryabhatta, one of the greatest mathematicians and astronomers of India in the fifth century AD, examined the astronomical evidence described in the Mahabharata in his great work known as the "Aryabhattiya". According to the positions of the planets recorded in the Mahabharata, its approximate date was calculated by Aryabhatta to be 3100 BC implying that the great war described in the Mahabharata was fought approximately 5000 years ago, as most Hindus have always believed. Exhibit 1 Approximate Positions of the Saptarshis (August 1990) Between the current location of the Saptarishis and the position mentioned in the Bhagvat, i.e., the Magha nakshatra, twenty three lunar mansions intervene, from Anuradha to Ashlesha, if the direction of movement opposite to the commonly accepted interpretation of the predictions made in the Bhagvat is followed (Exhibit 2). This direction of movement is equally likely since no records are available to establish the exact direction the saptarshis have historically followed.
Timeline: Eighth Century 750 CE arabian mathematicians begin using numbers that originated in India, are an advance of Roman numerals and that Muslims will pass to Europeans. http://www.fsmitha.com/h3/time08.html
Extractions: timeline index, from 60,000 bce CE Drawing from the Chinese and Confucianism, the Japanese have established new laws the Taiho Code. The emperor is seen as having supreme moral authority, a benevolent ruler, with moral ministers and bureaucrats, to whose authority otherwise feuding local lords should submit for the sake of peace. And, accompanying this centralized authority, a national tax system is devised. CE Empress Wu has proclaimed a new dynasty of her own family line. She has lowered taxes for farmers, and agricultural production has risen. She has strengthened public works. But by 705 she is in her old age and has lost control at court. Officicals at court force her to reisgn in favor of a member of the Tang family the return of the Tang Dynasty. CE In China, boiled war is safer to drink than untreated water, and tea becomes popular accompanied by the belief that tea has medicinal properties. CE Japan's emperor moves the capital from Osaka to the city of Nara in order to avoid the pollution of his predecessor's death.
CUBE These problems were also attacked by the arabian mathematicians; Tobit ben Korra (836901) is credited with a solution, while Abul Gud solved it by means of a http://82.1911encyclopedia.org/C/CU/CUBE.htm
Extractions: CUBE All these solutions were condemned by Plato on the ground that they were mechanical and not geometrical, i.e. they were not effected by means of circles and lines. However, no proper geometrical solution, in Platos sense, was obtained; in fact it is now generally agreed that, with such a restriction, the problem is insoluble. The pursuit of mechanical methods furnished a stimulus to the study of mechanical loci, for example. the locus of a point carried on a rod which is caused to move according to a definite rule. Thus Nicomedes invented the conchoid (q.v.); Diodes the cissoid (q.v.); Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form, of Pascals limaon (q.v.). These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola. In algebra, the cube of a quantity is the quantity multiplied by itself twice, i.e. if abe the quantity aXaXa(=af) is its cube. Similarly the cube root of a quantity is another quantity which when multiplied by itself twice gives the original quantity; thus ai is the cube root of a (see ARITHMETIC and ALGEBRA). A cubic equation is one in which the highest power of the unknown is the cube (see EQUATION); similarly, a cubic curve has an equation containing no term of a power higher than the third, the powers of a compound term being added together.
Science, Civilization And Society There is plenty of evidence that the arabian mathematicians used the system inherited from India to make significant progress in mathematics. http://www.es.flinders.edu.au/~mattom/science society/lectures/lecture6.html
Science, Civilization And Society learning. arabian mathematicians combined Greek geometry with Indian arithmetic and developed advanced algebra. Arabian physicians http://www.es.flinders.edu.au/~mattom/science society/lectures/lecture16.html
F.A.Z. - English Version Leonardo da Vinci had later worked with it as well as with a pair of compasses from the geometry room, which arabian mathematicians had developed in the 10th http://www.faz.com/IN/INtemplates/eFAZ/docmain.asp?rub={B1311FFE-FBFB-11D2-B228-
ThyssenKrupp VDM Metal Times the sixth decimal point. It took another thousand years for arabian mathematicians to do the same. The first instrument for registering http://www.metaltimes.de/MT27/E_Artikel-04.aspx
Extractions: Printing; the magnetic compass; gunpowder; suspension bridges; paddle steamers; ingenious technology for constructing furnaces, firing clay and processing metal; paper; the sternpost rudder; paper money, and so on â¦ These were known in the Middle Kingdom long before Europeans had even heard of them: A journey into Chinaâs technical history. Be that as it may, Marco Polo certainly influenced later generations. Europeans of his day could read the most comprehensive description they had ever had of the mysterious Chinese Empire. And when Christopher Columbus set off for America in 1492, he had Marco Poloâs âMilioneâ on board â just like the compass, which Chinese craftsmen had invented in the 4th century BCE and Arabian merchants had brought to the West in the 13th century. A piece of magnetic iron, decoratively carved into a ladle, on a smoothly polished stone slab â that is presumably mankindâs first compass looked like. The spoonâs handle pointed south while its mass, in this case its bowl, was drawn to the magnetic North Pole. This instrument, first referred to in writing as âSinanâ in 80 BCE, is thought to have served as orientation for far-travelling jade prospectors as early as the 4th century BCE. In mediaeval China, compasses were already working with magnetic needles, produced in series by special workshops. The earliest written reference to a marinerâs compass dates from the year 1113.