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13 relations: Archimedes, Geometric series, History of mathematics, Limit of a sequence, Mathematics, Reductio ad absurdum, Self-similarity, Series (mathematics), Sierpinski triangle, Similarity (geometry), Square, The Quadrature of the Parabola, Triangle.
Archimedes
Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
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Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
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History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Reductio ad absurdum
In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.
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Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts).
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Sierpinski triangle
The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
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Similarity (geometry)
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.
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Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
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The Quadrature of the Parabola
The Quadrature of the Parabola (Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC.
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Triangle
A triangle is a polygon with three edges and three vertices.
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1 + 1/4 + 1/16 + 1/64 + 1/256 + · · ·, 1/4 + 1/16 + 1/64 + 1/256 + ..., 1/4 + 1/16 + 1/64 + 1/256 + · · ·, 1/4th geometric infinite series, ¼ + 1/16 + 1/64 + 1/256 + ….
References
[1] https://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_⋯
