Category Archive: Non-Euclidean Geometries

Oct 14

Rational Geometry: A Text-Book for the Science of Space;

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Evolutionstheorie und ihre Evolution. [16] Book I Proposition 27 of Euclid's Elements [17] see (Trudeau 1987) [18] Imre Toth. His Klein's Quartic curve and popularly-famous Klein's bottle were among several useful results from his new approaches to groups and higher-dimensional geometries and equations. These revolutionary discoveries inspired Plücker, and were declared by Gauss to be "among the most revolutionary intuitions in the history of mathematics." However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.

Oct 14

Killer Mine

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MaxFEM users can perform internal changes to both the interface and the contained calculus programs in order to adapt the software to their needs. McCarthy, from his article "The toxins of William B. His fame lives on and even the lower-case word 'abelian' is applied to several concepts. Clifford was a versatile and talented mathematician who was among the first to appreciate the work of both Riemann and Grassmann. Transformation optics grew out of ideas for invisibility cloaking devices and exploits connections between electromagnetism in media and in geometries.

Oct 14

The Foundations of Geometry

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That was met with almost universal hostility and ridicule and disbelief by other scientists. ... This means that the classical additive derivative is undefined because the difference f(x+deltax)-f(x) has no value. Euclid's Elements contained five postulates which form the basis for Euclidean geometry. Semmelweis discovered that the incidence of puerperal fever (also known as "childbed fever") could be drastically cut by the use of hand disinfection in obstetrical clinics. ...

Oct 14

100 Worksheets - Finding Face Values with 4 Digit Numbers:

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Non-Newtonian calculus was used in the article "On line and double integrals in the non-Newtonian sense" by Ahmet Faruk Çakmak (Yıldız Technical University in Turkey) and Feyzi Başar (Fatih University in Turkey). [201] From the Abstract: "This paper is devoted to line and double integrals in the sense of non-Newtonian calculus (*-calculus). Hyperbolic lines are infinite in length since their endpoints lie on the circle and points on the circle are considered infinitely far away.

Oct 14

The Elements of Non-Euclidean Geometry (Dover Books on

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William Dunham as quoted in his book Journey Through Genius (1990). "On the back page of his book of logarithms, Gauss recorded the discovery of his formula for the number of primes up to N in terms of the logarithm function. Operations regarding polynomials, exponents, and radicals. The Poincar� compromise is to represent angles truly while distorting scale. Motivated by the discussion around Theorem C (see also [ 34 ]), let us define the typical spacing Λ as the inverse of the positive number \(\frac {\mathbb{E}[ \mathcal{N}_{\varSigma} ]}{

Oct 13

Global Affine Differential Geometry of Hypersurfaces (De

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The Riemann integral and the first form of the Fundamental Theorem of Calculus are introduced. He tried to prove it using a reductio ad absurdum argument. They fought, they suffered and they paid. You could define it as the Pythagorean distance — i.e. sqrt(Xdif*Xdif + Ydif*Ydif), which in this case would be sqrt(8*8+6*6) = 10 — but that would be an arbitrary presumption of Euclidean geometric rules. The meta-calculi can be used for financial-investment analysis, and are discussed in our book Meta-Calculus: Differential and Integral (1981).

Oct 13

Commensurabilities among Lattices in PU (1,n). (AM-132)

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Riemann's other masterpieces include tensor analysis, the theory of functions, and a key relationship between some differential equation solutions and hypergeometric series. A., was severely handicapped in an accident, and then switched to pure mathematics. So, it should come as no surprise that when I was given an opportunity to speak at Singularity Summit last fall, a conference largely concerned with exponential trends in technology, I decided to try to persuade people of the utility of multiplicative calculus and the value of mathematical abstractions." (The expression "multiplicative calculus" refers here to the geometric calculus.) - Christopher Olah, Thiel Fellow; from Christopher Olah's Blog, 07 May 2013. [134, 135, 164] "In this [project] you will explore alternative 'calculi'.

Oct 13

A Gateway to Modern Geometry: The Poincare Half-Plane

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Michael Grossman and Robert Katz. "Isomorphic calculi", International Journal of Mathematical Education in Science and Technology, Volume 15, Issue 2, pages 253-263, DOI:10.1080/0020739840150214, Taylor and Francis, 1984. To accept cookies from this site, use the Back button and accept the cookie. But Reader is to be really commended for using the Moore method course to create a means to master it quickly, effectively and without trying to cover 5 terms of material on one semester the way some of the other examples of this type course listed here do.

Oct 13

The Fifth Postulate: How Unraveling A Two Thousand Year Old

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But some people objected to the article, saying that NNC was "not notable". In many practical problems the main interest lies not in pointwise reconstruction of the true density but rather in answering qualitative questions, for instance about the number of modes or the regions of increase and decrease. This time-dependent and nonlinear set of partial differential equations describes a wealth of phenomena in laser physics but remains rather difficult to solve. That gave two observationally equivalent solar theories based on two quite different mechanisms.

Oct 13

Riemannian Holonomy Groups and Calibrated Geometry (Oxford

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Additive and multiplicative differentials and integrals of dialectical judgements" by Leonid G. By use of methods of multiplicative calculus it is proved that an infinitely-many times differentiable function may not be analytic." (The expression "multiplicative calculus" refers here to the geometric calculus.) Application of the bigeometric derivative to the theory of elasticity in economics was made by Fernando Córdova-Lepe (Universidad Católica del Maule in Chile). (He referred to the bigeometric derivative as the "multiplicative derivative.") [3, 4, 105] Elasticity is also discussed in Non-Newtonian Calculus [15], Bigeometric Calculus: A System with a Scale-Free Derivative [10], and The First Systems of Weighted Differential and Integral Calculus [9].

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