Topic
AA postulate
About: AA postulate is a research topic. Over the lifetime, 6 publications have been published within this topic receiving 29 citations.
Papers
TL;DR: Evidence is provided for a novel illusion where an angle embedded in an isosceles triangle is judged substantially larger than the same angles embedded in a scalene triangle, demonstrating that mechanisms for computing angles are sensitive to the context within which angles are presented.
22 citations
TL;DR: It is shown constructively that the euclidean plane can be tiled using integral triangles no two of which are similar.
5 citations
TL;DR: The maximum number of congruent triangles in finite arrangements of l lines in the Euclidean plane is studied and four conjectures about which integers c there exist arrangements on l lines with exactly c congruant triangles are formulated.
Abstract: We study the maximum number of congruent triangles in finite arrangements of l lines in the Euclidean plane. Denote this number by f (l) . We show that f (5) = 5 and that the construction realizing this maximum is unique, f (6) = 8 , and f (7) = 14 . We also discuss for which integers c there exist arrangements on l lines with exactly c congruent triangles. In parallel, we treat the case when the triangles are faces of the plane graph associated to the arrangement (i.e. the interior of the triangle has empty intersection with every line in the arrangement). Lastly, we formulate four conjectures.
3 citations
1 Jan 2005
TL;DR: In this article, pairwise congruent empty triangles were used for pattern construction in the pairwise Congruent Empty Triangle Pattern (COPT) pattern, and Pach's number was assigned to the pattern.
Abstract: Keywords: pairwise congruent empty triangles ; pattern Note: Professor Pach's number: [195] Reference DCG-ARTICLE-2005-002 Record created on 2008-11-14, modified on 2017-05-12
2 citations
TL;DR: In this article, the authors adopt the following classification for a Euclidean planar, purely based on angles alone: a planar triangle is said to be acute if all the three angles of the planar are acute angles.
Abstract: This article adopts the following classification for a Euclidean planar , purely based on angles alone. A Euclidean planar triangle is said to be acute angled if all the three angles of the Euclidean planar are acute angles. It is said to be right angled at a specific vertex, say B, if the angle is a right angle with the two remaining angles as acute angles. It is said to be obtuse angled at the vertex B if is an obtuse angle, with the two remaining angles as acute angles. In spite of the availability of numerous text books that contain our human knowledge of Euclidean plane geometry, softwares can offer newer insights about the characterizations of planar geometrical objects. The author's characterizations of triangles involve points like the centroid G, the orthocentre H of the , the circumcentre S of the , the centre N of the nine-point circle of the . Also the radical centre rc of three involved diameter circles of the sides BC, AC and AB of the provides a reformulation of the orthocentre, resulting i...
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2013 | 1 |
| 2008 | 1 |
| 2006 | 1 |
| 2005 | 1 |
| 1974 | 1 |