# Elementary Surprises in Projective Geometry

## Related Articles

- A very simple proof of Pascal's hexagon theorem and some applications. Stefanović, Nedeljko; Milošević, Miloš // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Nov2010, Vol. 120 Issue 5, p619
In this article we present a simple and elegant algebraic proof of Pascal's hexagon theorem which requires only knowledge of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding an equation of the conic containing five given...

- Brianchon's theorem (1806) Mathematics. // Dictionary of Theories;2002, p67
A definition of the term "Brianchon's theorem" is presented. This mathematical theorem proposes that if a hexagon is circumscribed about a conic, its three diagonals are concurrent. The theorem, named after Charles-Julien Brianchon, can also be deduced from Pascal's mystic hexaghram theorem.

- Triangles and Parallelograms of Equal Area Inside the Hyperbola. ROMASKO, ADAM M.; OSLER, THOMAS J. // Mathematical Spectrum;2009/2010, Vol. 42 Issue 2, p70
The article discusses the property of the hyperbola, which is based on a paper by Euler that revealed the shared properties of general curves and those of conic sections. In trying to find the triangles inside a hyperbola, the diameter is the line M M1 as it is the one that passes through the...

- Why are surjective lineations of the Archimedean hyperbolic plane motions? Pambuccian, V. // Acta Mathematica Hungarica;2003, Vol. 100 Issue 1/2, p63
Positive LÏ‰1Ï‰ definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary...

- CACTUS: The ubiquitous parabola. Hyde, Hartley // Australian Mathematics Teacher;Aug2008, Vol. 64 Issue 3, p7
The article provides information on how to use Cabri Geometry in studying the parabola as a conic section and the use of Cabri 3D in constructing a circular paraboloid. The author stated that the activity will show that the locus of all the points are equi-distant from a line and a point....

- Strange Duality for Parabolic Symplectic Bundles on a Pointed Projective Line. Abe, Takeshi // IMRN: International Mathematics Research Notices;Jan2008, Vol. 2008, p1
We prove the strange duality for parabolic symplectic bundles on a pointed projective line.

- OVOIDS OF PG(3,q), q EVEN, WITH A CONIC SECTION. BROWN, MATTHEW R. // Journal of the London Mathematical Society;10/01/2000, Vol. 62 Issue 2, p569
It is shown that if a plane of PG(3,q), q even, meets an ovoid in a conic, then the ovoid must be an elliptic quadric. This is proved by using the generalized quadrangles T2(5) (5 a conic), W(q) and the isomorphism between them to show that every secant plane section of the ovoid must be a...

- High-Order Parametric Polynomial Approximation of Conic Sections. Jaklič, Gašper; Kozak, Jernej; Krajnc, Marjeta; Vitrih, Vito; Žagar, Emil // Constructive Approximation;Aug2013, Vol. 38 Issue 1, p1
In this paper, a particular shape preserving parametric polynomial approximation of conic sections is studied. The approach is based upon the parametric approximation of implicitly defined planar curves. Polynomial approximants derived are given in a closed form and provide the highest possible...

- POÄ°NCARÃ‰ KONÄ°KLERÄ°NÄ°N DENKLEMLERÄ° VE SINIFLANDIRILMASI. SÖNMEZ, Nilgün // Afyon Kocatepe University Journal of Science;2008, Vol. 8 Issue 1, p63
No abstract available.