Complex Vectors and Image Identification

Autoencoder framework based on orthogonal projection constraints improves anomalies detection

(2000). Artemas Martin: An Amateur Mathematician of the Nineteenth Century and His Contribution to Mathematics. The College Mathematics Journal: Vol. 31, No. 1, pp. 22-34.

(1996). Another Way to Graph a Sequence. The College Mathematics Journal: Vol. 27, No. 3, pp. 208-209.

(1999). Recounting Fibonacci and Lucas Identities. The College Mathematics Journal: Vol. 30, No. 5, pp. 359-366.

(1990). Tabular Integration by Parts. The College Mathematics Journal: Vol. 21, No. 4, pp. 307-311.

(2007). A Geometric View of Complex Trigonometric Functions. The College Mathematics Journal: Vol. 38, No. 3, pp. 210-217.

(2000). Finding Unpredictable Behavior in a Simple Ordinary Differential Equation. The College Mathematics Journal: Vol. 31, No. 5, pp. 338-346.

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsMartin GardnerApart from compilations of his Mathematical Games columns, more than 70 other books Martin Gardner has written concern science, philosophy, and literature, the best known being The Annotated Alice, a study of Lewis Carroll's two books about Alice. The Flight of Peter Fromm, and Visitors from Oz, are novels. Gardner has also edited several anthologies of popular verse.Gardner's lifelong hobby is conjuring, about which he has written books for the trade. As his good friend Persi Diaconis has written, “Warning: Martin Gardner has turned hundreds of mathematicians into magicians and hundreds of magicians into mathematicians.”Gardner currently lives in Norman, Oklahoma and is as active writing as ever.

(1985). Inverse Hyperbolic Functions as Areas. The College Mathematics Journal: Vol. 16, No. 2, pp. 129-131.

(2005). Curious Consequences of a Miscopied Quadratic. The College Mathematics Journal: Vol. 36, No. 4, pp. 273-277.

(2003). The Eccentricity of a Conic Section. The College Mathematics Journal: Vol. 34, No. 2, pp. 116-121.

(1985). Accurate Computation of Variance. The College Mathematics Journal: Vol. 16, No. 2, pp. 149-150.

(1985). Bernoulli's Inequality and the Number e. The College Mathematics Journal: Vol. 16, No. 5, pp. 399-400.

The classical isoperimetric inequality relates the lengths of curves to the areas that they bound. More specifically, we have that for a smooth, simple closed curve of length L bounding area A on a surface of constant curvature c, L 2 ≥ 4πA – cA 2 with equality holding only if the curve is a geodesic circle. We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic wave fronts (i.e. piecewise smooth curves which may have cusps). We then discuss “bicycle curves” using the generalized isoperimetric inequalities. The euclidean model of a bicycle is a unit segment AB that can move so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame), as discussed in [Finn, The College Mathematics Journal, 33, 2002], [Tabachnikov, Israel J. Math. 151: 1–28, 2006], and [Levi, Tabachnikov, Experiment. Math. 18: 173–186, 2009]. We extend this definition to a general Riemannian manifold, and concern ourselves in particular with bicycle curves in the hyperbolic plane H 2 and on the sphere S 2. We prove results along the lines of those in [Levi, Tabachnikov, Experiment. Math. 18: 173–186, 2009] and resolve both spherical and hyperbolic versions of Menzin's conjecture, which relates the area bounded by a curve to its associated monodromy map.

(1998). Colored Polygon Triangulations. The College Mathematics Journal: Vol. 29, No. 1, pp. 43-47.