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In this right triangle: sin A = a/h; cos A = b/h; tan A = a/b. Trigonometric ratios are the ratios between edges of a right triangle. These ratios depend only on one acute angle of the right triangle, since any two right triangles with the same acute angle are similar. [31]
Circle packing in a circle – Two-dimensional packing problem; Circle packing in an equilateral triangle – Two-dimensional packing problem; Circle packing in an isosceles right triangle – Two-dimensional packing problem; Circle packing theorem – Describes the possible tangency relations between circles with disjoint interiors
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
If we draw both circles, two new points are created at their intersections. Drawing lines between the two original points and one of these new points completes the construction of an equilateral triangle. Therefore, in any geometric problem we have an initial set of symbols (points and lines), an algorithm, and some results.
The Erdős–Oler conjecture: when is a triangular number, packing circles in an equilateral triangle requires a triangle of the same size as packing circles. [ 47 ] The disk covering problem abount finding the smallest real number r ( n ) {\displaystyle r(n)} such that n {\displaystyle n} disks of radius r ( n ) {\displaystyle r(n)} can be ...
Circles G to J, which do not, map to other circles. The reference circle and line L map to themselves. Circles intersect their inverses, if any, on the reference circle. In the SVG file, click or hover over a circle to highlight it. Inversion of a line is a circle containing the center of inversion; or it is the line itself if it contains the ...