A Golden Triangle is a triangle with two of its sides in the ratio (J>:1, where is the Fibonacci Ratio, i.e., (J> = ^(1 + /J) ^ 1.618. Let AABC be a triangle whose sides are a,b, and o and let a/b = k > 1. Bicknell and Hoggatt [1] have shown that (1) a triangle with a side equal to b can be removed from AABC to leave a triangle similar to AABC if and only if k = cj), and (2) a triangle simi...

This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crack-clos...

Methods of linear algebra are applied to triangle geometry. The vertex triangle of distinct circumcevian triangles is proved to be perspective to the reference triangle ABC, and similar results hold for three other classes of vertex triangles. Homogeneous coordinates of the perspectors define four mappings Mi on pairs of points (U, X). Many triangles homothetic to ABC are examined, and properti...

Deep reinforcement learning is an emerging machine approach which can teach a computer to learn from their actions and rewards similar the way humans experience. It offers many advantages in automating decision processes navigate large parameter spaces. This paper proposes novel efficient measurement of quantum devices based on deep learning. We focus double dot devices, demonstrating fully aut...

Toshiaki Fujiwara†, Hiroshi Fukuda‡, Atsushi Kameyama§, Hiroshi Ozaki¶ and Michio Yamada* † College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 228-8555, Japan ‡ School of Administration and Informatics, University of Shizuoka, 52-1 Yada, Shizuoka 422-8526, Japan § Department of Mathematical and Design Engineering, Faculty of Engineering, Gifu Univer...

We present a method to adaptively refine an irregular triangle mesh as it deforms in real-time. The method increases surface smoothness in regions of high deformation by splitting triangles in a fashion similar to one or two steps of Loop subdivision. The refinement is computed for an arbitrary triangle mesh and the subdivided triangles are simply passed to the rendering engine, leaving the mes...

The Fourier transform of a skeletal delta function that characterizes the most striking features of experimental quasi-crystal diffraction patterns is evaluated. The result plays a role analogous to the Poisson summation formula for periodic delta functions that underlie classical crystallography. The real-space distribution can be interpreted in terms of a backbone comprising a system of inter...