Golden Mean, The
| Publication Language |
English |
|---|---|
| Publication Type |
eBooks |
| Publication License Type |
Open Access |
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Essay on the Foundations of Geometry, An
Bertrand Russell was a prolific writer, revolutionizing philosophy and doing extensive work in the study of logic. This, his first book on mathematics, was originally published in 1897 and later rejected by the author himself because it was unable to support Einstein's work in physics. This evolution makes An Essay on the Foundations of Geometry invaluable in understanding the progression of Russell's philosophical thinking. Despite his rejection of it, Essays continues to be a great work in logic and history, providing readers with an explanation for how Euclidean geometry was replaced by more advanced forms of math. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).
Euler?s Number. Why Is Eule’s Number “E” the Basis of Natural Logarithm Functions
Document from the year 2016 in the subject Mathematics - Miscellaneous, grade: A, , course: IB Math HL, language: English, abstract: When the concept of logarithms was first introduced to me, a plethora of questions revolved around my mind. My inquisitiveness compelled me to think and ask questions as to where are the practical applications of logarithms, why do we take different bases of these functions and what is the need for natural logarithms. Amongst these questions, one particularly intrigued me: why is e particularly the base of the natural logarithm. Why out of all numbers that exist did we choose e as the base of the natural logarithm function? I was fascinated by why taking the base e made the normal logarithm a natural logarithm. Therefore, to quench the curiosity of many others like me, I will show through this paper that why e is the correct choice for the base of exponential and natural logarithm functions. I shall also be exploring the most important property of e, via this paper.
Pi
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The Way to Geometry
Plato saith "tov peov akei gewmetreiv", That "God doth alwayes worke by Geometry", that is, as the wiseman doth interprete it, Sap. XI. 21. Omnia in mensura & numero & pondere disponere. Dispose all things by measure, and number, and weight: Or, as the learned Plutarch speaketh; He adorneth and layeth out all the parts of the world according to ra-te, proportion, and similitude. Now who, I pray you, understandeth what these termes meane, but he which hath some meane skill in Geometry? Therefore none but such an one, may be able to declare and teach these things unto ot-hers. How many things are there in holy Scripture which may not well be understood without some meane skill in Geometry? The Fabricke and bignesse of Noah's Arke: The Sciagraphy of the Temple set out by Ezechiel, Who may understand, but he that is skilfull in these Arts? I speake not of many and sundry words both in the New and Old Testaments, whose genuine and proper signification is merely Geometricall: And cannot well be conceived but of a Geometer. To the Reader: Friendly Reader, that which is here set forth to thy view, is a Translation out of Ramus. Formerly indeed Translated by one Mr. Thomas Hood, but never before set forth with the Demonst-rations and Diagrammes, which being cut before the Authors death, and the Worke it selfe finished, the Coppie I having in mine hands, never had thought for the promulgation of it, but that it should have died with its Author, considering no small prejudice usually attends the printing of dead mens Workes, and wee see the times, the world is now all eare and tongue, the most given with the Athenians, to little else than to heare and tell newes: And if Apelles that skilfull Artist alwayes found so-mewhat to be amended in those Pictures which he had most curiously drawne; surely much in this Worke might have beene amended if the Authour had lived to refine it..
