TITLE

# Geometric Constructions with Ellipses

AUTHOR(S)
Gibbins, Aliska; Smolinsky, Lawrence
PUB. DATE
January 2009
SOURCE
Mathematical Intelligencer;Winter2009, Vol. 31 Issue 1, p65
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The article discusses the concept of geometric constructions with ellipses. It outlines the primary concerns with solid constructions. Regarding geometric construction, it is called planar if it is done with straightedge and compass alone, solid if it uses conic sections and linear if it uses higher order curves.
ACCESSION #
36277569

## Related Articles

• A GENERALIZED ARCHIMEDEAN PROPERTY. Bényi, Árpád; Van Vleck, Fred; Szeptycki, Pawel // Real Analysis Exchange;2003/2004, Vol. 29 Issue 2, p881

We introduce and discuss a condition generalizing one of the Archimedean properties characterizing parabolas.

• The Parabola.  // Monkeyshines on Health & Science;Jan97 Mathematics & Health, p8

One of the most useful geometric curves is the parabola. Every parabola has two important parts: its focus point and its axis. Paraboloids are very useful objects and are found all around. They are used in two important ways for sending and for receiving. In sending, if a light source is placed...

• WHITNEY CURVES REVISITED. Cs&#xouml;rnyei, Marianna; Kališ, Jan; Zajíček, Luděk // Real Analysis Exchange;June2005 Conference, p95

Describes the curve function computed by Whitney. Definition of critical and Whitney arcs; Iterative method that gives an example of a Whitney arc.

• A SPECIAL SPIRAL: THE COCHLEOID. Luca, Liliana; Popescu, Iulian // Fiability & Durability / Fiabilitate si Durabilitate;2011, Issue 1, p13

They are shown geometrical considerations and properties of cochleoid, which is a flat curve from the spiral's family. Are established various mathematical relations, which are useful when drawing the curves. They are given examples of different drawn cochleoid.

• Spacelike Normal Curves in Minkowski Space ?13. Ilarslan, Kazim // Turkish Journal of Mathematics;2005, Vol. 29 Issue 1, p53

In the Euclidean space Eï¿½, it is well known that normal curves, i.e., curves with position vector always lying in their normal plane, are spherical curves [3]. Necessary and sufficient conditions for a curve to be a spherical curve in Euclidean 3-space are given in [10] and [11]. In this...

• THE MODULI SPACES OF BIELLIPTIC CURVES OF GENUS 4 WITH MORE BIELLIPTIC STRUCTURES. G. CASNATI; A. DEL CENTINA // Journal of the London Mathematical Society;Jun2005, Vol. 71 Issue 3, p599

Let \\$C\\$ be an irreducible, smooth, projective curve of genus \\$g\$\backslash\$geqslant 3\\$ over the complex field \\$\$\backslash\$mathbb\{C\}\\$. The curve \\$C\\$ is called \{\$\backslash\$em bielliptic\} if it admits a degree-two morphism \\$\$\backslash\$pi\$\backslash\$colon C\$\backslash\$longrightarrow...

• Dynamics Near an Unstable Kirchhoff Ellipse. Guo, Yan; Hallstrom, Chris; Spirn, Daniel // Communications in Mathematical Physics;Mar2004, Vol. 245 Issue 2, p297

We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general...

• Another Geometric Vision of the Hyperbola. OSLER, THOMAS J. // Mathematical Spectrum;2009, Vol. 41 Issue 3, p123

The article presents information on the two methods that are commonly used in defining the hyperbola. As stated, the two definitions relate to each other on the conic sections and construction of the hyperbola is dependent on the asymptotes of the curve. Equations and graphs on the construction...

• Existence of homographic solutions in non-Newtonian dynamics. Grebenikov, E. A.; Diarova, D. M.; Zemtsova, N. I. // AIP Conference Proceedings;2/10/2011, Vol. 1329 Issue 1, p124

The idea of the Wintner method relate to the problem of existence in the Newtonian many body problem of homographical solutions, similar to conic sections. We have generalised this idea on a case of other classes of homographical solutions, similar to curves, described by the Wejerstrass function.

Share