The Math That Explains Why Bell Curves Are Everywhere | Quanta Magazine The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day.

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Three-Distance Theorem : Let α ∈ (0, 1) be irrational and let N be a positive integer. Then the set of lengths {kα | 0 ≤ k ≤ N}, measured around the unit-circumference circle, partitions the circle into N + 1 intervals, whose lengths take just two values, or three values of which one is the sum of the other two.

Theorem of the Day (March 16, 2026) : The Three-Distance Theorem
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/NumberTheory...
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Praeger’s Theorem on Bounded Movement : Let G be a permutation group acting without fixed points on a set Ω. Denote by m the maximum size of any subset Γ ⊆ Ω whose image under some group element is disjoint from Γ; and suppose that m is finite. Then Ω is a finite set; the number t of G orbits is at most 2m − 1; each orbit has length at most 3m; and |Ω| ≤ 3m + t − 1 ≤ 5m − 2.

Theorem of the Day (March 15, 2026) : Praeger’s Theorem on Bounded Movement
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. Pick’s Theorem : Let P be a simple polygon (i.e. containing no holes or separate pieces) whose vertices lie on the points of a rectangular lattice. Suppose that I lattice points are located in the interior of P and B lattices points lie on the boundary of P. Then the area of P is given by K = I + B/2 − 1

Theorem of the Day (March 14, 2026) : Pick’s 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. De Moivre’s Theorem : Let θ be an angle and n a positive integer. Then (cos θ + i sin θ)^n = cos nθ + i sin nθ.

Theorem of the Day (March 13, 2026) : De Moivre’s 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. Countability of the Rationals : There is a one-to-one correspondence between the set of positive integers and the set of positive rational numbers.

Theorem of the Day (March 12, 2026) : Countability of the Rationals
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. Brahmagupta’s Formula : The area K of a cyclic quadrilateral with side lengths a, b, c, d and semiperimeter s = (a + b + c + d)/2 is given by K = √((s − a)(s − b)(s − c)(s − d)).

Theorem of the Day (March 11, 2026) : Brahmagupta’s Formula
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/uITdf6I

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Riemann Rearrangement Theorem : If ∑_(k=0)^∞ a_k is a series which is conditionally convergent, and c is any real number, then the terms of the series may be rearranged to give convergence to c, i.e. there is a permutation π of the nonnegative integers such that ∑ a_(π(k)) = c.

Theorem of the Day (March 10, 2026) : The Riemann Rearrangement 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 Fundamental Theorem of Arithmetic : Every integer greater than one can be expressed uniquely (up to order) as a product of powers of primes.

Theorem of the Day (March 9, 2026) : The Fundamental Theorem of Arithmetic
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. Singmaster’s Binomial Multiplicity Bound : For integer k > 1, let N(k) denote the multiplicity of k as a binomial coefficient; i.e. N(k) =∣{(n, r) ∈ Z^2 : k = "n choose r"}∣. Then N(k) = O(log k).

Theorem of the Day (March 8, 2026) : Singmaster’s Binomial Multiplicity Bound
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/JA1MRg1

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : Viète’s Formula.

Theorem of the Day (March 7, 2026) : Viète’s Formula
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. Kepler’s Conjecture : Any packing of three-dimensional Euclidean space with equal-radius spheres has density bounded by τ √2/12 ≈ 0.74.

Theorem of the Day (March 6, 2026) : Kepler’s Conjecture
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/nclvnzQ
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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Kasteleyn’s Theorem : Suppose that G is a planar graph drawn in the plane. Then 1. we can orient the edges so that every face has an odd number of clockwise-oriented edges, and 2. if A(G) is the signed adjacency matrix of such an orientation of G then number of perfect matchings of G = √det(A(G)).

Theorem of the Day (March 5, 2026) : Kasteleyn’s 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 Bruck-Ryser-Chowla Theorem : If a projective plane of order n exists, with n ≡ 1 or 2 (mod 4) then n = x^2 + y^2 for some integers x and y.

Theorem of the Day (March 4, 2026) : The Bruck-Ryser-Chowla Theorem
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/NrrOUxL

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The Six Circles Theorem illustrated janmr.com/posts/six-ci... #math #visualization #geometry #theorem

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Erdos–Ko–Rado Theorem : Let n and k be positive integers, with n ≥ 2k. In a set of cardinality n, a family of distinct subsets of cardinality k, no two of which are disjoint, can have at most "(n-1) choose (k-1)" members.

Theorem of the Day (March 3, 2026) : The Erdos–Ko–Rado Theorem
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/CfDI0yp

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Ramanujan Partition Congruences : Let n be a non-negative integer and let p(n) denote the number of partitions of n (that is, the number of ways to write n as a sum of positive integers). Then p(n) satisfies the congruence relations: p(5t + 4) ≡ 0 ( mod 5), p(7t + 5) ≡ 0 ( mod 7), and p(11t + 6) ≡ 0 ( mod 11).

Theorem of the Day (March 2, 2026) : The Ramanujan Partition Congruences
Source : Theorem of the Day / Robin Whitty
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SQL vs. NoSQL: The Database Decision That Separates Senior Engineers From the Rest The SQL vs. NoSQL interview question tests far more than database knowledge. It reveals how engineers reason about...

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[Original post on webpronews.com]

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Vaughan Pratt’s Theorem : Primality testing is in NP.

Theorem of the Day (March 1st, 2026) : Vaughan Pratt’s 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. Sharkovsky’s Theorem : Specify an ordering, ≺, of the positive integers: 3, 5, 7, 9, . . . , 2×3, 2×5, 2×7, 2×9, . . . , 2^2 ×3, 2^2 ×5, 2^2 ×7, 2^2 ×9, . . . . . . , 2^4, 2^3, 2^2, 2^1, 1, defined formally as follows: take x < y with x and y written (uniquely) as x = 2^r p and y = 2^s q, p, q odd; then x ≺ y if r ≤ s and p > 1; otherwise y ≺ x. Now let f : R → R be a continuous function having a point x of period m; that is, f^m(x) = f (x), where f^m denotes the m-th iteration of f . Then for every n with m ≺ n, f has some point of period n. In particular, if f has a point of period 3, then f has periods of all positive integer orders.

Theorem of the Day (February 28, 2026) : Sharkovsky’s Theorem
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/wlV6wjZ

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Taylor’s Theorem : Let c be a real number and f a real-valued function which is (n+1)-times differentiable in some interval I around c. Then for x ∈ I, there is some value θ lying between x and c, such that f (x) = f (c) + f ′(c)(x − c) + f ′′(c)(x − c)^2 / 2! + . . . + f^(n)(c) (x − c)^n / n! + f^ (n+1)(θ) (x − c)^(n+1) / (n + 1)! .

Theorem of the Day (February 27, 2026) : Taylor’s Theorem
Source : Theorem of the Day / Robin Whitty
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Archimedes' Twin Circles Illustrated janmr.com/posts/archim... #math #visualization #geometry #theorem

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Chinese Remainder Theorem : Suppose n1, n2, . . . , nr are mutually coprime positive integers (that is, no integer greater than 1 dividing one may divide any other.) Let y1, y2, . . . , yr be any integers. Then there is a number x whose remainder on division by ni is yi, for each i. That is, the system of linear congruences x ≡ yi (mod ni) has a solution. Moreover this solution is unique modulo N = n1 × n2 × . . . × nr.

Theorem of the Day (February 26, 2026) : The Chinese Remainder Theorem
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/c04ZtTF

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : The Andrews–Garvan–Dyson Crank.

Theorem of the Day (February 25, 2026) : The Andrews–Garvan–Dyson Crank
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. Theaetetus’ Theorem on the Platonic Solids : There are precisely five regular convex polyhedra, namely the Platonic solids: the tetrahedron, cube, octahedron, icosahedron and dodecahedron

Theorem of the Day (February 24, 2026) : Theaetetus’ Theorem on the Platonic Solids
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/CsHOdhg

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Euclid’s Infinity of Primes : There are infinitely many prime numbers.

Theorem of the Day (February 23, 2026) : Euclid’s Infinity of Primes
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. Strassen’s Matrix Theorem : Two n × n matrices can be multiplied in fewer than n^3 (multiplication) steps.

Theorem of the Day (February 22, 2026) : Strassen’s Matrix 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 Convolution Theorem : Let a = (a_0, . . . , a_n) and b = (b_0, . . . , b_n) be vectors in C^(n+1). The convolution of a and b, denoted a⋆b, is the vector c = (c_0, . . . , c_(2n)), in C^(2n+1), defined by c_i = ∑_(j=0)^n a_j b_(i− j), i = 0, . . . , 2n, with b_k = 0 whenever k < 0 or k > n. Then a ⋆ b = F ^(−1) (F (a) • F (b)), where F is the (2n + 1)-dimensional Discrete Fourier Transform and • is componentwise multiplication.

Theorem of the Day (February 21, 2026) : The Convolution 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. Pappus’ Theorem : Let A, B, C and a, b, c be two sets of collinear points. Let A be joined by a line to b and c; B to a and c; and C to a and b. Then the intersection points of the line pairs Ab with Ba, Ac with Ca and Bc with Cb are again collinear.

Theorem of the Day (February 20, 2026) : Pappus’ Theorem
Source : Theorem of the Day / Robin Whitty
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notes : buff.ly/rMO8T0m

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Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Intermediate Value Theorem : Let f (x) be a real-valued function which is continuous on the closed interval [a, b] and such that f (a) < f (b). Then for any value y0 satisfying f (a) < y0 < f (b), there is a value x0 satisfying a < x0 < b for which f (x0) = y0.

Theorem of the Day (February 19, 2026) : The Intermediate Value Theorem
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/Analysis/IVT...
notes : www.theoremoftheday.org/Resources/Th...

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