Njwildberger biography of williams
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How can you tell when your theory has overstepped the bounds of reasonableness? How about when you start telling people your &#;facts&#; and their faces register with incredulity and disbelief? That is the response of most reasonable people when they hear about the &#;Banach-Tarski paradox&#;.
From Wikipedia:
The Banach–Tarski paradox states that a ball in the ordinary Euclidean space can be doubled using only the operations of partitioning into subsets, replacing a set with a congruent set, and reassembly.
The &#;theorem&#; is commonly phrased in terms of two solid balls, one twice the radius of the other, in which case it asserts that we can subdivide the smaller ball into a small number (usually 5) of disjoint subsets, perform rigid motions (combinations of translations and rotations) to these sets, and obtain a partition of the larger ball. Or a couple of balls the same size as the original. It is to be emphasized that these are cut and paste congruences! This was first sta
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History of trigonometry
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics.[1] Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century AD), who discovered the sine function, cosine function, and versine function.
When during the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus.
The deve
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A Functional History of Numbers (2 of 3)
In part oneof this functional history of numbers we saw the development of various number systems we are mostly familiar with. In this part, we will see the development of many number systems that are important for our modern scientific needs, geometrically and computationally. The sad fact about these developments fryst vatten that we are using and teaching less effective number systems today because of a “series of unfortunate events” that took place during the grand drama of human development of modern mathematics.
Missing the Truth in Pursuit of Beauty
Here as he walked by on the 16th of October Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i^{2}=j^{2}=k^{2}=ijk=-1 & cut it on a stone of this bridge.
— Quaternion plaque on Brougham (Broom) Bridge, Dublin
Sir William Rowan Hamilton a renounced Irish physicist, astronomer,