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In the visual arts, shape is a flat, enclosed area of an artwork created through lines, textures, or colours, or an area enclosed by other shapes, such as triangles, circles, and squares. [1] Likewise, a form can refer to a three-dimensional composition or object within a three-dimensional composition. [2]
Draw three circumcircles (Miquel's circles) to triangles AB´C´, A´BC´, and A´B´C. Miquel's theorem states that these circles intersect in a single point M, called the Miquel point. In addition, the three angles MA´B, MB´C and MC´A (green in the diagram) are all equal, as are the three supplementary angles MA´C, MB´A and MC´B. [2] [3]
A cutaway drawing is a technical illustration, in which part of the surface of a three-dimensional model is removed in order to show some of the model's interior in relation to its exterior. The purpose of a cutaway drawing is to "allow the viewer to have a look into an otherwise solid opaque object.
An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides, and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
Malfatti's assumption that the two problems are equivalent is incorrect. Lob and Richmond (), who went back to the original Italian text, observed that for some triangles a larger area can be achieved by a greedy algorithm that inscribes a single circle of maximal radius within the triangle, inscribes a second circle within one of the three remaining corners of the triangle, the one with the ...
In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last quarter of the nineteenth century. Triangles and their properties were the subject of investigation since at least the time of Euclid.
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