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When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and two vertices of the starting triangle all have the same perimeter. [4] Triangles whose outer Soddy circle degenerates to a straight line with curvature zero have been called "Soddyian triangles ...
A Heronian triangle is commonly defined as one with integer sides whose area is also an integer. The lengths of the sides of such a triangle form a Heronian triple (a, b, c) for a ≤ b ≤ c. Every Pythagorean triple is a Heronian triple, because at least one of the legs a, b must be even in a Pythagorean triple, so the area ab/2 is an integer.
In geometry, the isoperimetric point is a triangle center — a special point associated with a plane triangle.The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly in 1985 to denote a point P in the plane of a triangle ABC having the property that the triangles PBC, PCA, PAB have isoperimeters, that is, having the property that [1] [2]
The Soddy line of a triangle is the line that goes through the centers of the two Soddy circles of that triangle. The Soddy line intersects the Euler line in the de Longchamps point and the Gergonne line in the Fletcher point. It is also perpendicular to the Gergonne line and together all three lines form the Euler-Gergonne-Soddy triangle. The ...
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In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.
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An Atlanta burger brand will open its first NC restaurants, including a Triangle location. Popular NY shop known for ‘deliciously overstuffed sandwiches’ will open in Raleigh.
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