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Posts tagged #theorem

Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
23 hours ago
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

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
pdf : buff.ly/IlPfcat
notes : buff.ly/R1AjXKZ

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 day ago
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.

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
pdf : buff.ly/ADn1ujE
notes : buff.ly/hKorjqZ

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 days ago
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.

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
pdf : buff.ly/e4IJiYa
notes : buff.ly/fqDjJbQ

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 days ago
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)).

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
pdf : buff.ly/SvBNXmR
notes : buff.ly/uITdf6I

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
4 days ago
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.

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
pdf : buff.ly/fnN4vpA
notes : buff.ly/0G72KAO

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
5 days ago
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.

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
pdf : buff.ly/HyCAVdL
notes : buff.ly/hJxskAz

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
6 days ago
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).

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
pdf : buff.ly/68VtkiC
notes : buff.ly/JA1MRg1

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : Viète’s Formula.

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
pdf : buff.ly/U64te0w
notes : buff.ly/36wtRF4

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
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.

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
pdf : buff.ly/3855EnW
notes : buff.ly/nclvnzQ
#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
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)).

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
pdf : buff.ly/IbGFiRS
notes : buff.ly/jt8wX9k

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
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.

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
pdf : buff.ly/kcz0V6o
notes : buff.ly/NrrOUxL

#mathematics #maths #math #theorem

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Jan Marthedal Rasmussen
Jan Marthedal Rasmussen
@janmr.com
1 week ago
Post image

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

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
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.

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
pdf : buff.ly/JWVMGyl
notes : buff.ly/CfDI0yp

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
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).

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
pdf : buff.ly/SSzrQBd
notes : buff.ly/nMY9VUS

#mathematics #maths #math #theorem

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PostgreSQL
PostgreSQL
@postgresql.activitypub.awakari.com.ap.brid.gy
1 week ago
Original post on webpronews.com

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...

#BigDataPro #ACID #transactions #CAP #theorem #database […]

[Original post on webpronews.com]

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
1 week ago
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Vaughan Pratt’s Theorem : Primality testing is in NP.

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
pdf : buff.ly/dloSVGx
notes : buff.ly/QEn2ssT

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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.

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
pdf : buff.ly/WB8W6nB
notes : buff.ly/wlV6wjZ

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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)! .

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
pdf : buff.ly/QnYQGMd
notes : buff.ly/OIK51B7

#mathematics #maths #math #theorem

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Jan Marthedal Rasmussen
Jan Marthedal Rasmussen
@janmr.com
2 weeks ago
Post image

Archimedes' Twin Circles Illustrated janmr.com/posts/archim... #math #visualization #geometry #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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.

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
pdf : buff.ly/nVl5JUI
notes : buff.ly/c04ZtTF

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : The Andrews–Garvan–Dyson Crank.

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...

#mathematics #maths #math #theorem

1 1 0 0
Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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

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
pdf : buff.ly/8t0CCK4
notes : buff.ly/CsHOdhg

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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.

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
pdf : buff.ly/Os3cQ7R
notes : buff.ly/bYYoyMZ

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
2 weeks ago
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.

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
pdf : buff.ly/kej1yzX
notes : buff.ly/Fi0djWa

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 weeks ago
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.

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
pdf : buff.ly/d6EvqJo
notes : buff.ly/TGSsbBr

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 weeks ago
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.

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
pdf : buff.ly/Qq11eK5
notes : buff.ly/rMO8T0m

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 weeks ago
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.

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...

#mathematics #maths #math #theorem

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 weeks ago
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The BEST Theorem : Let G = (V, E) be a directed graph in which, for each vertex v in V, the indegree and outdegree have the same value, d(v), say. Then G has a directed Euler tour: a closed walk which passes each edge exactly once; let ε(G) denote the number of such tours. Then, for any fixed vertex x, ε(G) = tx ∏_(v∈V) (d(v) − 1)! where tx denotes the number of those spanning trees of G in which every vertex has a directed path to x.

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The BEST Theorem : Let G = (V, E) be a directed graph in which, for each vertex v in V, the indegree and outdegree have the same value, d(v), say. Then G has a directed Euler tour: a closed walk which passes each edge exactly once; let ε(G) denote the number of such tours. Then, for any fixed vertex x, ε(G) = tx ∏_(v∈V) (d(v) − 1)! where tx denotes the number of those spanning trees of G in which every vertex has a directed path to x.

Theorem of the Day (February 18, 2026) : The BEST Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/aZjB8Em
notes : buff.ly/YaUg32w

#mathematics #maths #math #theorem

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Scandal Questions
Scandal Questions
@scandalquestions.bsky.social
3 weeks ago

Quine is a philosophy.
If we would think of them from the mathematical side, they're like system which breaks Gödel's theorem about incompleteness.

The system creates itself with its axioms without external help.

Is it wonderful?

#math #quine #godel #axiom #theorem #philosophy

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Paysages Mathématiques
Paysages Mathématiques
@paysmaths.bsky.social
3 weeks ago
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Irrationality of Circumference of Unit Circle : The circumference, τ, of the unit circle is not rational, i.e. it cannot be expressed as a ratio of two integers.

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Irrationality of Circumference of Unit Circle : The circumference, τ, of the unit circle is not rational, i.e. it cannot be expressed as a ratio of two integers.

Theorem of the Day (February 17, 2026) : Irrationality of Circumference of Unit Circle
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/NumberTheory...
notes : www.theoremoftheday.org/Resources/Th...

#mathematics #maths #math #theorem

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