The triangle is an integral part of the history economic thought. It has been used by writers such as Jevons (1871), Taussig (1896), Wicksell (1934, 1969) to illustrate and help us understand capital theory. Since Hayek (1931) this geometrical figure a basic pedagogical device explain Austrian Business Cycle Theory (ABCT). purpose present paper argue that highly problematic, if not fatally flaw...

The paper investigates a hypothesis that our visual system groups visual cues based on how they form a surface, or more specifically triangulation derived from the visual cues. To test our hypothesis, we compare shape recognition with three different representations of visual cues: a set of isolated dots delineating the outline of the shape, a set of triangles obtained from Delaunay triangulati...

We investigate the problem of cutting a triangle ABC into N congruent triangles (the “tiles”), which may or may not be similar to ABC. We wish to characterize the numbers N for which some triangle ABC can be tiled by N tiles, or more generally to characterize the triples (N,T ) such that ABC can be N-tiled using tile T . In the first part of the paper we exhibit certain families of tilings whic...

What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordinates as independent standard Gaussians. Six can be reduced to four by transl...

For given triangles T = (A,B,C) and D = (X, Y, Z), the D-Napoleon and D-Torricelli triangles ND(T ) and TD(T ) of a triangle T = (A,B,C) are the triangles A′B′C ′ and A∗B∗C∗, where ABC ′, BCA′, CAB′, A∗BC, AB∗C, ABC∗ are similar to D. In this paper it is shown that the iteration N n D(T ) either terminates or converges (in shape) to an equilateral triangle, and that the iteration T n D (T ) eit...

We consider the set of triangles in the plane with rational sides and a given area A. We show there are infinitely many such triangles for each possible area A. We also show that infinitely many such triangles may be constructed from a given one, all sharing a side of the original triangle, unless the original is equilateral. There are three families of triangles (including the isosceles ones) ...

— Copy-move forgery is one of the most common types of tampering for digital images. Detection methods generally use block-matching approaches, which first divide the image into overlapping blocks and then extract and compare features to find similar ones, or point-based approaches, in which relevant keypoints are extracted and matched to each other to find similar areas. In this paper we prese...

Processing of line- and luminance-defined triangles was investigated by studying visual potentials (VEPs) evoked by triangles. Twenty-six subjects were randomly presented with line, grey, and illusory triangles. Relative to VEPs elicited by grey and illusory triangles, VEPs to line triangles included P220s that were smaller at frontal sites but larger at occipital sites, and N260s that were sma...

We investigate the phase behavior of a system of hard equilateral and right-angled triangles in two dimensions using Monte Carlo simulations. Hard equilateral triangles undergo a continuous isotropic-triatic liquid crystal phase transition at packing fraction ϕ = 0.7. Similarly, hard right-angled isosceles triangles exhibit a first-order phase transition from an isotropic fluid phase to a rhomb...