[6] **viXra:1602.0270 [pdf]**
*submitted on 2016-02-21 13:29:33*

**Authors:** Bogdan Szenkaryk "Pinopa"

**Comments:** 1 Page. Contact the Author - ratunek.nauki(at)onet.pl

The article comprises equation even more beautiful than Euler's identity, which is considered the most beautiful math equation. The equation is even more beautiful, because from it is derived Euler's identity. Besides, there can be derived from it many other no less beautiful mathematical identities as Euler's.

**Category:** Geometry

[5] **viXra:1602.0269 [pdf]**
*submitted on 2016-02-21 13:31:46*

**Authors:** Bogdan Szenkaryk "Pinopa"

**Comments:** 1 Page. Contact the Author - ratunek.nauki(at)onet.pl

Novelty which earlier - before it appears - no one saw; the beautiful equation.

**Category:** Geometry

[4] **viXra:1602.0252 [pdf]**
*submitted on 2016-02-20 11:33:33*

**Authors:** Robert B. Easter

**Comments:** 12 Pages.

This paper gives an overview of two different, but closely related, double conformal geometric algebras. The first is the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), and the second is the G(4,8) Double Conformal Space-Time Algebra (DCSTA). DCSTA is a straightforward extension of DCGA. The double conformal geometric algebras that are presented in this paper have a large set of operations that are valid on general quadric surface entities. These operations include rotation, translation, isotropic dilation, spacetime boost, anisotropic dilation, differentiation, reflection in standard entities, projection onto standard entities, and intersection with standard entities. However, the quadric surface entities and other "non-standard entities" cannot be intersected with each other.

**Category:** Geometry

[3] **viXra:1602.0249 [pdf]**
*submitted on 2016-02-20 04:32:07*

**Authors:** Orgest ZAKA, Kristaq FILIPI

**Comments:** 9 Pages.

In this paper, based on several meanings and statements discussed in the literature, we intend
constuction a affine plane about a of whatsoever corps (K,+,*). His points conceive as
ordered pairs (α,β), where α and β are elements of corps (K,+,*). Whereas straight-line in
corps, the conceptualize by equations of the type x*a+y*b=c, where a≠0K or b≠0K the
variables and coefficients are elements of that body. To achieve this construction we prove
some theorems which show that the incidence structure A=(P, L, I) connected to the corps
K satisfies axioms A1, A2, A3 definition of affine plane. In all proofs rely on the sense of the
corps as his ring and properties derived from that definition.

**Category:** Geometry

[2] **viXra:1602.0234 [pdf]**
*replaced on 2016-03-08 16:32:26*

**Authors:** Espen Gaarder Haug

**Comments:** 19 Pages.

Squaring the Circle is a famous geometry problem going all the way back to the ancient Greeks. It is the great quest of constructing a square with the same area as a circle using a compass and straightedge in a finite number of steps. Since it was proved that pi was a transcendental number in 1882, the task of Squaring the Circle has been considered impossible. Here, we will show it is possible to Square the Circle in Euclidean space-time. It is not possible to Square the Circle in Euclidean space alone, but it is fully possible in Euclidean space-time, and after all we live in a world with not only space, but also time. By drawing the circle from one reference frame and drawing the square from another reference frame, we can indeed Square the Circle. By taking into account space-time rather than just space the Impossible is possible! However, it is not enough simply to understand math in order to Square the Circle, one must understand some “basic” space-time physics as well. As a bonus we have added a solution to the impossibility of Doubling the Cube. As a double bonus we also have also boxed the sphere! As one will see one can claim we simply have bent the rules and moved a problem from one place to another. One of the main essences of this paper is that we can move challenging space problems out from space and into time, and vice versa.

**Category:** Geometry

[1] **viXra:1602.0074 [pdf]**
*submitted on 2016-02-06 11:14:56*

**Authors:** editor Florentin Smarandache

**Comments:** 156 Pages.

In the new Techno-Art of Selariu SuperMathematics Functions ALBUM (the second book of Selariu SuperMathematics Functions), one contemplates a unique COMPOSITION, INTER-, INTRA- and TRANS-DISCIPLINARY. A comprehensive and savant INTRODUCTION explains the genesis of the inserted "figures", the addressees being, without discriminating criteria, equally engineers, mathematicians, artists, graphic designers, architects, and all lovers of beauty – as the love of beauty is the supreme form of love. If I should put a label on the "content" of this ALBUM, I would concoct the word NEO-BEAUTY!
The new complements of mathematics, reunited under the name of ex-centric mathematics (EM), extend (theoretically, endless) their scope; in this respect, Selariu SuperMathematics Functions are undeniable arguments! The author has labored (especially in the last three decades) extensively and fruitfully in the elitist field of the domain.
To mention some 'milestones' in this ALBUM, I choose specific mathematical elements, supermatematically hybridated: quadrilobic cubes, sphericubes, conopyramids, ex-centric spirals, severed toroids. There are also those that would qualify as "utilitarian": clepsydras, vases, baskets, lampions, or those suggestively “baptized” (by the author): butterflies, octopuses, flying saucers, jellies, roundabouts, ribands, and so on – all superlatively designed in shapes and colors! Striking phrases, such as “staggering multiplication of the dimensions of the Universe”, “integration through differential division” etc., become plausible (and explained) by replacing the time (of Einstein's four-dimensional space) with ex-centricity. Consequently, classical geometrical bodies (for e=0): the sphere, the cylinder, the cone, undergo metamorphosis (for e = +/-1), respectively into a cube, a prism, a pyramid. Inevitably and invariably, it is confirmed again that science is a finite space that grows in the infinite space; each new "expansion" does include a new area of unknown, but the unknown is inexhaustible...
Just browsing the ALBUM pages, you feel induced by the sensation of pleasure, of love at first sight; the variety of "exhibits", most of them unusual, the elegance, the symmetry of the layout, the chromatic, and so one, delight the eye, but equally incites to catchy intellectual exploration.

**Category:** Geometry