Latest posts tagged with #theorem on Bluesky
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : The Eratosthenes–Legendre Sieve.
Theorem of the Day (April 8, 2026) : The Eratosthenes–Legendre Sieve
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Fundamental Theorem of Algebra : The polynomial equation of degree n: z^n + a_1 z^(n−1) + . . . + a_(n−1)z + a_n = 0, with n ≥ 1 and with the a_i belonging to C, the complex numbers, has a solution in C. As a consequence, the polynomial can be factorised as (z − α1)(z − α2) · · · (z − αn), where the αi are again in C and are precisely the roots of the polynomial.
Theorem of the Day (April 7, 2026) : The Fundamental Theorem of Algebra
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. A Theorem on Apollonian Circle Packings : For every integral Apollonian circle packing there is a unique ‘minimal’ quadruple of integer curvatures, (a, b, c, d), satisfying a ≤ 0 ≤ b ≤ c ≤ d, a+b+c+d > 0 and a + b + c ≥ d. This so-called root quadruple completely specifies the packing.
Theorem of the Day (April 6, 2026) : A Theorem on Apollonian Circle Packings
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Five Circle Theorem : Let the five sides of a pentagon ABCDE be extended until they intersect in five points P, Q, R, S and T , say. Then the five circumcircles of triangles BQA, APE, ETD, DSC and CRB intersect with each other in five distinct points, not lying on the pentagon and lying on a common circle.
Theorem of the Day (April 5, 2026) : The Five Circle Theorem
Source : Theorem of the Day / Robin Whitty
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#mathematics #maths #math #theorem
"Heure : -100 s Sol : 0 Heure : -90 s Jour : 0 Heure : -89 s Humains : 0 Heure : -85 s"
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Generalised Hexachord Theorem : Suppose that S is a subset of the set of pitch classes comprising Zn, n even, with |S | = s; then the interval class vectors of S and its complement Zn \ S differ component-wise by |n − 2s|, except for the last component, for which the difference is |n/2 − s|.
Theorem of the Day (April 4, 2026) : The Generalised Hexachord Theorem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Stable Marriage Theorem : Suppose n women rank n men in order of preference. The men, likewise, rank the n women. Then there exists a stable marriage: a pairing of the women and men such that no pair exists who would rather be married to each other than to their assigned partners.
Theorem of the Day (April 3, 2026) : The Stable Marriage Theorem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Lutz-Nagell Theorem : For the elliptic curve y^2 = x^3 + ax^2 + bx + c, with a, b, and c integers and having (non-zero) discriminant function D = −4a^3c + a^2b^2 + 18abc − 4b^3 − 27c^2, let P = (X, Y) be a rational point of finite order greater than 1. Then X and Y are integers and either Y divides D or Y = 0 and P has order 2.
Theorem of the Day (April 2, 2026) : The Lutz-Nagell Theorem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Remainder Theorem : If a polynomial f (x) is divided by (x − α) then the remainder is f (α). Corollary (The Factor Theorem) : A polynomial f (x) has (x − α) as a factor if and only if f (α) = 0.
Theorem of the Day (April 1st, 2026) : The Remainder Theorem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Gruenberg’s Theorem on Nilpotent Groups : A finitely generated, torsion-free, nilpotent group is a residually finite p-group, for every prime p.
Theorem of the Day (March 31, 2026) : Gruenberg’s Theorem on Nilpotent Groups
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Pappus–Guldin Theorems : Suppose that a plane curve is rotated about an axis external to the curve. Then 1. the resulting surface area of revolution is equal to the product of the length of the curve and the displacement of its centroid; 2. in the case of a closed curve, the resulting volume of revolution is equal to the product of the plane area enclosed by the curve and the displacement of the centroid of this area.
Theorem of the Day (March 30, 2026) : The Pappus–Guldin Theorems
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Theorema Egregium : The Gaussian curvature of surfaces is preserved by local isometries.
Theorem of the Day (March 29, 2026) : Theorema Egregium
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Euler’s Formula : For any real or complex value of θ, e^(iθ) = cos θ + i sin θ.
Theorem of the Day (March 28, 2026) : Euler’s Formula
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/GeometryAndT...
notes : www.theoremoftheday.org/Resources/Th...
#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Wallis’s Product : The value of τ/4 (τ = 2π) is given by the infinite product ∏_(k=1)^∞ (2k)^2 / ((2k − 1)(2k + 1)) = 2^2/(1.3). 4^2/(3.5). 6^2/(5.7) . . . .
Theorem of the Day (March 27, 2026) : Wallis’s Product
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. 1-Factorisation of Regular Graphs : There exists a constant, c, such that all simple d-regular graphs of even order, n, with cn ≤ d, have a 1-factorisation.
Theorem of the Day (March 26, 2026) : 1-Factorisation of Regular Graphs
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Bondy’s Subset Theorem : Let S be a set with n elements and suppose that n distinct subsets of S are chosen. Then there is a restriction to n − 1 elements of S under which these subsets remain distinct.
Theorem of the Day (March 25, 2026) : Bondy’s Subset Theorem
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/InformationT...
notes : www.theoremoftheday.org/Resources/Th...
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Girard–Newton Identities : For a fixed set S of variables, denote by e_k, 0 ≤ k ≤ |S |, the k-th elementary symmetric polynomial in the variables of S ; that is e_k = ∑_(X⊂S, |X|=k) ∏_(x∈X) x, with e_0 = 1. Denote by p_k the k-th power sum over S ; that is p_k = ∑_(x∈S) x^k. Then the following recurrence holds: ke_k = ∑_(i=1)^k (−1)^(i−1) p_i e_(k−i), for k ≥ 1.
Theorem of the Day (March 24, 2026) : The Girard–Newton Identities
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : The Change of Variables Theorem.
Theorem of the Day (March 23, 2026) : The Change of Variables Theorem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Handshaking Lemma : In any graph the sum of the vertex degrees is equal to twice the number of edges.
Theorem of the Day (March 22, 2026) : The Handshaking Lemma
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/Combinatoria...
notes : www.theoremoftheday.org/Resources/Th...
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : Integration By Parts.
Theorem of the Day (March 21, 2026) : Integration By Parts
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Fifteen Theorem : If a positive-definite quadratic form defined by a symmetric, integral matrix takes each of the values 1, 2, 3, 5, 6, 7, 10, 14, 15, then it takes all positive integer values.
Theorem of the Day (March 20, 2026) : The Fifteen Theorem
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/NumberTheory...
notes : www.theoremoftheday.org/Resources/Th...
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Basel Problem : 1 + 1 / 4 + 1 / 9 + . . . = ∑_(k=1)^∞ (1 / k^2) = τ^2 / 24.
Theorem of the Day (March 19, 2026) : The Basel Problem
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Euler’s Partition Identity : The number of partitions of a positive integer n into distinct parts is equal to the number of partitions of n into odd parts.
Theorem of the Day (March 18, 2026) : Euler’s Partition Identity
Source : Theorem of the Day / Robin Whitty
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Tunnell’s Theorem : Let n be a square-free positive integer and denote by S_n(a, b, c) the number of solutions in integers, x, y, z, of the equation ax^2 + by^2 + cz^2 = n. Then a necessary condition for n to be a congruent number is that S_n(2, 1, 8) = 2S_n(2, 1, 32) n odd and S_n(8, 2, 16) = 2S_n(8, 2, 64) n even . Moreover, if the Birch and Swinnerton-Dyer conjecture is true then this condition is also sufficient.
Theorem of the Day (March 17, 2026) : Tunnell’s Theorem
Source : Theorem of the Day / Robin Whitty
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