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Topic: Eulers formula

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	Euler's formula - Wikipedia, the free encyclopedia
		Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that shows a deep relationship between the trigonometric functions and the complex exponential function.
		Euler's formula was proven (in an obscured form) for the first time by Roger Cotes in 1714, then rediscovered and popularized by Euler in 1748.
		Euler's formula provides a powerful connection between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function:
	en.wikipedia.org /wiki/Euler's_formula (846 words)

	Eulers formula in complex analysis - Wikipedia
		Euler's formula allows one to interpret the sine and cosine functions as mere variations of the exponential function:
		The most remarkable formula in the world is an easy consequence of Euler's formula.
		In electrical engineering and other fields, signals that vary periodically over time are often described as a combination of sine and cosine functions (see Fourier analysis), and these are more conveniently expressed as exponential functions with imaginary exponents, using Euler's formula.
	nostalgia.wikipedia.org /wiki/Eulers_formula_in_complex_analysis (416 words)

	De Moivre's formula - Wikipedia, the free encyclopedia
		The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometry.
		By expanding the left hand side and then comparing the real and imaginary parts, it is possible to derive useful expressions for cos(nx) and sin(nx) in terms of cos(x) and sin(x).
		Abraham de Moivre was a good friend of Newton; in 1698 he wrote that the formula had been known to Newton as early as 1676.
	en.wikipedia.org /wiki/De_Moivres_formula (420 words)

	Gresham College \| Transcript
		Euler worked in an astonishing variety of areas, ranging from the very pure the theory of numbers, the geometry of a circle and musical harmony via such areas as infinite series, logarithms, the calculus and mechanics, to the practical optics, astronomy, the motion of the Moon, the sailing of ships, and much else besides.
		Euler found himself in physics, rather than medicine, which was probably a relief for all those future patients who might not have appreciated being operated on with straight-edge and compass.
		Euler proved, using his generating functions, that for any number, the number of odd partitions is always equal to the number of distinct partitions an intriguing and unexpected result.
	www.gresham.ac.uk /printtranscript.asp?EventId=67 (3517 words)

	Lesson Plans--Euler's Formula (Site not responding. Last check: 2007-09-21)
		Students will discover Euler's formula for polyhedra, and will be able to show that it works for any convex polyhedron.
		This formula is named "Euler's Formula" (pronounced "oiler") after the Swiss mathematician Leonhard Euler who discovered this relationship in 1752.
		Euler showed that his formula works for any convex polyhedron, whether it is regular or irregular.
	www.cs.rockhurst.edu /~brandt/lesson/euler.html (664 words)

	PlanetMath: Euler relation
		Euler's relation (also known as Euler's formula) is considered the first bridge between the fields of algebra and geometry, as it relates the exponential function to the trigonometric sine and cosine functions.
		This is version 9 of Euler relation, born on 2001-11-08, modified 2005-06-02.
		Proof of Euler's Relation using Taylor's Series by DJ Craig on 2005-06-06 17:15:56
	planetmath.org /encyclopedia/EulerRelation.html (152 words)

	Euler's Formula
		This page lists proofs of the Euler formula: for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.
		According to Malkevitch, this formula was discovered in around 1750 by Euler, and first proven by Legendre in 1794.
		Perhaps there is a proof of Euler's formula that uses these polynomials directly rather than merely translating one of the inductions into polynomial form.
	www.ics.uci.edu /~eppstein/junkyard/euler (615 words)

	Body (Site not responding. Last check: 2007-09-21)
		Euler analysis applies to slender columns, the formula, for the critical axial concentric load that causes the column to be on the point of collapse for frictionless pinned ends (no bending moment at the ends) is given below.
		Eulers equation as written can be applied to a column with ends fixed in any manner if the length is taken as that between sections of zero bending moment.
		A typical factor of safety, or design factor, for Euler structural columns is between 2 and 3.5, but this is based on the critical load, not on the yield or ultimate strength of the material.
	www.tech.plymouth.ac.uk /sme/desnotes/buckling.htm (640 words)

	De Moivre's formula - Free net encyclopedia (Site not responding. Last check: 2007-09-21)
		De Moivre's formula states that for any real number x and any integer n,
		When n = 0 the formula is true since $\cos(0x) + i\sin(0x) = 1 + i0 = 1$ , and (by convention) $z^{0} = 1$ .
		Euler's formula Root of unityar:صيغة دي مويفير cs:Moivreova věta da:De Movires formel es:Fórmula de De Moivre fr:Formule de Moivre it:Formula di De Moivre nl:Stelling van De Moivre ja:ド・モアブルの定理 pl:Wzór de Moivre'a pt:Fórmula de de Moivre sr:Моаврова формула fi:De Moivren kaava zh:棣美弗定理
	www.netipedia.com /index.php/De_Moivre's_formula (480 words)

	e^i.pi = - 1 (Site not responding. Last check: 2007-09-21)
		Eulers derivation is both concise and beautiful, it contains three extremely important mathematical constants, e, i and π which can be explored in turn by clicking the relevant area of the formula above.
		However, the mathematics behind this formula, which I hope shall become clear to you is rock-solid, and its conclusion can not be doubted.
		The modulus-arguement form of a complex number used to derive Eulers formula is very useful as it makes multiplication and division of a complex number simple.
	www.bath.ac.uk /~pb242/Euler1.html (332 words)

	Chief Delphi - A really odd math problem....
		This is known as eulers formula, and I personally find it to be the craziest and most profound thing I've ever seen.
		Euler's formula is pretty famous (well among engineers and mathematicians, anyway).
		The formula for the area of a regular polygon, where A = area, N = the number of sides, and L = the length of each side, is:
	www.chiefdelphi.com /forums/showthread.php?p=276077 (1266 words)

	e (Site not responding. Last check: 2007-09-21)
		If you haven't guessed from the title this page is about the constant e (or 2.7182818284...) which is named in honour of the swiss mathematician Leohard Euler who was born in basel in 1707 and made many important contribution to the study of mathematics through out his life.
		Anyway back to the actual subject at hand e is probally one of the must useful and important numbers there is with it appearing in a wide range of areas of mathematics from complex numbers to differential equations.
		In addition to Eulers formula providing a useful representation for complex numbers it can also be used to derive linking equations for sinh(x)-sin(x)and cosh(x)-cos(x)as I will demonstrate below for sinh(x) and sin(x):
	people.bath.ac.uk /acb23/e2.html (556 words)

	Homologi och Eulerkarakteristik
		Originally the Euler characteristic was defined by triangulation and Eulers formula.
		The reason for this is that the Euler characteristic also can be computed using homology groups.
		In this essay we describe the connection between these two means of calculating the Euler characteristic.
	epubl.luth.se /avslutade/1103-4483/95-02 (74 words)

	Complex number problem
		using eulers formula express cos5ø in terms of cosø.
		And using eulers formula we cant have angles different for the cos and sine terms..
		De Moivre's formula is useful when you are dealing with powers and roots of complex numbers.
	www.physicsforums.com /showthread.php?t=118250 (683 words)

	[No title]
		\layout Remark \begin_inset Formula $\left(i,j\right)$ \end_inset is an adjacent pair of \begin_inset Formula $\left(k,l\right)$ \end_inset iff \begin_inset Formula $gcd\left(k-i,l-j\right)=1$ \end_inset.
		\layout Subsection Eulers formula \layout Standard \begin_inset Formula $n$ \end_inset nodes in a graph \layout Standard \begin_inset Formula $e$ \end_inset edges \layout Standard \begin_inset Formula $f$ \end_inset faces (including \begin_inset Quotes eld \end_inset the rest of the plane \begin_inset Quotes erd \end_inset) \layout Standard then \begin_inset Formula $n+f=e+2$ \end_inset.
		\begin_deeper \layout Claim Also if we insert \begin_inset Formula $m$ \end_inset inner points \end_deeper \layout Claim And the number of triangles in such a triangulation is \begin_inset Formula $n+2m-2$ \end_inset \layout Subsection The integer grid \layout Standard \begin_inset Formula $\Z^{2}$ \end_inset is generated by integer combinations of a basis with two vectors.
	www.technion.ac.il /~danielv/lectures/AppliedGeometry/lectures.lyx (1424 words)

	Grade Level: 9-12
		Explain to the students that there are several different types of objects that have many numbers of sides and they encounter them in their daily lives.
		I will then draw a polyhedron on the board and then calculate it sides using Euler’s formula.
		To check for comprehension I will as the students what a polyhedron is and ask someone to tell me how to do Euler’s formula.
	www.redrockdata.com /matportfolio/files/Lp_math_3.htm (452 words)

	Second moment opf area/buckling
		The formula involves the second moment of area of the shape, initially a
		And how good a guide is Eulers formula, how good an agreement might I expect
		Euler supposes that the column fails by buckling at LESS than the
	www.groupsrv.com /science/post-1184732.html (1157 words)

	Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills - The Right Gift For Him (Site not responding. Last check: 2007-09-21)
		It is well-written and the text flows marvelously between each page and around the many formulas that are so carefully presented and worked out.
		I rate this book as 5-stars for presenting ever more mathematics relating to complex numbers in a clear and detailed manner.
		The reviews of An Imaginary Tale capture much of what will be said of Dr. Euler's Fabulous Formula.
	www.therightgiftforhim.com /store/asinsearch_0691118221 (241 words)

	History and Current Status of the Plastics Industry
		Euler formula is not valid for Inelastic buckling
		J.B. Johnson formula is valid for inelastic buckling
		Parabola that connects Eulers Formula line to the short column
	www.csuchico.edu /~jpgreene/cm197/cm197_ch19-03_files/v3_slide0099.htm (34 words)

	Can You Find by Shyam Sunder Gupta (Site not responding. Last check: 2007-09-21)
		My "C" implementation of his formula and the answer to this problem is below.
		In searching for primes of the form ax^2+bx+c, it is good to put the axis of symmetery at -b/2a=50000.5 so that when x yields a prime value then 100001-x also yields a prime value (what we Americans call a "two-fer," for two for one sales).
		The general principle is sound but one should realize that, once a candidate formula is found, the value at x=1 might be composite while the value at x=100001 might be prime, so that shifting x by 1 would up the prime count.
	www.shyamsundergupta.com /canyoufind.htm (4718 words)

	Gresham College \| Search Lectures & Events (Site not responding. Last check: 2007-09-21)
		Euler, ‘the Mozart of mathematics’, was probably the most prolific mathematician of all time, having contributed to many areas, both theoretical and practical, both serious and recreational – yet he remains largely unknown except to mathematicians.
		Who was he, what did he do, and why do mathematicians regard him so highly?
		If you experience any problems listening to this clip, try the standalone RealPlayer.
	www.gresham.ac.uk /event.asp?PageId=4&EventId=67 (3622 words)

	Amazon.com: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills: Books: Paul J. Nahin (Site not responding. Last check: 2007-09-21)
		The book is, as the author notes, a continuation of his book, An Imaginary Tale, where Nahin discusses the square root of -1.
		(If you haven't read that book, read it first because many of the footnotes refer to it.) In this book, we see more of complex numbers and, in particular, we see many applications of Euler's Identity that "e^{i theta} = cos(theta)+ i sin(theta)." This simple looking indentity is rich in applications and explorations.
		Nahin takes you on a journey to these topics and does so in an easy to follow way.
	www.amazon.com /exec/obidos/tg/detail/-/0691118221?v=glance (1274 words)

	MathLinks Math Forums :: View topic - Euler`s function... (Site not responding. Last check: 2007-09-21)
		MathLinks Math Forums :: View topic - Euler`s function...
		Find all numbers m such that Euler`s function of m divides m.
		the problem is straightforward from the formula for eulers function using the prime factorisation of n.
	www.mathlinks.ro /Forum/post-243541.html (254 words)

	MATH3050.06 Assignment 7: Euler's Formula. (Site not responding. Last check: 2007-09-21)
		(b) What we did in class, and what is on this page, give the essential steps ofthe proof of Euler's formula.
		Euler's formula can be adapted to 'polyhedra' which are not 'spherical' - but fit other kinds of surfaces (i.e.
		Can you state Euler's formula for several of these other surfaces?
	www.math.yorku.ca /Who/Faculty/Whiteley/3050_Ass7.html (304 words)

	Facets of Geometry (Site not responding. Last check: 2007-09-21)
		This is an outreach program that our science club has been successfully using over the last year.
		Facets of Geometry utilizes large polyhedra to explore the mathmatical relationship found in Eulers Formula: the number of facets plus the number of vertices minus the number of edges equals two.
		Using large foam rubber shapes students can verify for themselves the validity of this relationship.
	flux.aps.org /meetings/YR99/CENT99/abs/S5605013.html (111 words)

	Gauss Proof (urgend)
		How dou you arrive to that result from euler's formula?
		Cause if I insert the numbers into the formula I get the cos(2pi/5).
		and I insert v = (2 pi)/5 into euler which gives (sqrt(5) -1)/4.
	www.physicsforums.com /showthread.php?t=101199 (727 words)

	No Title
		Upon my approval present your report to the class.
		Topic examples: relativity, fractals, game theory, Eulers Formula V-E+F=2, prime numbers, graph theory, volume and surface area of n-dimensional spheres, encryption, etc.
		Report on an application of Calculus from your major field
	www.ma.utexas.edu /users/darrin/Courses/ESP/studproj/studproj.html (259 words)

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