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The solution in which two of the three rectangles are congruent and the third one has twice the side lengths of the other two, where the rectangles have aspect ratio 3:2. The solution in which the three rectangles are all of different sizes and where they have aspect ratio ρ 2.
The solution in which the three rectangles are all of different sizes and where they have aspect ratio ρ 2, where ρ is the plastic ratio. The fact that a rectangle of aspect ratio ρ 2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ρ 2 related to the Routh–Hurwitz ...
The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = 13×5 / 2 = 32.5 units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent.
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
Gou Gu dual capacity discusses algorithms for calculating the areas of the inscribed rectangles and other polygons in the circle, which also serves an algorithm to calculate the value of pi. Lastly, Gou Gu similars provide algorithms of calculating heights and lengths of buildings on the mathematical basis of similar right triangles.
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
A whirl of golden rectangles. Divide a square into four congruent right triangles with legs in ratio 1 : 2 and arrange these in the shape of a golden rectangle, enclosing a similar rectangle that is scaled by factor and rotated about the centre by ().
Packing different rectangles in a rectangle: The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an important application in combining images into a single larger image. A web page that loads a single larger ...