Lmst

White House in July, 2024: "We could classify any area of math we think is leading in a bad direction to make it a state secret and "it will end"."

My decomposition is a state secret.
Academia is 14 years late.

#decompwlj #FundamentalTheoremOfArithmetic #math #maths #mathematics #sequences #OEIS #NumberTheory #PrimeNumbers #JavaScript #php #graph #3D #classification #primes #threejs #webGL #integer #decomposition #numbers #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #academia #research #NSA #CIA #DGSE #DGSI #Google

Theorem of the Day (May 4, 2025) : Sylvester’s Law of Inertia
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Algebra/Sylvester/TotDSylvester.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#142

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : Sylvester’s Law of Inertia.

Theorem of the Day (May 3, 2025) : Machin’s Formula
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Binomial/Machin/TotDMachin.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#170

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Machin’s Formula : τ/8 = 4 tan^(−1) (1/5)− tan^(−1) (1/239) , where τ = 2π.

Theorem of the Day (May 2, 2025) : Lucas’ Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Binomial/Lucas/TotDLucas.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#38

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Lucas’ Theorem : Let p be a prime number and let a and b, a ≥ b, be positive integers written in base p, say, a = ∑_(i=0)^s a_i p^i and b = ∑_(j=0)^t b_j p^j and s ≥ t. Then
"a choose b" ≡ "a_0 choose b_0" "a_1 choose b_1"· · ·"a_(t−1) choose b_(t-1)" "a_t choose b_t" (mod p).

Theorem of the Day (May 1st, 2025) : Lamé’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Binomial/Lame/TotDLame.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#87

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Lamé’s Theorem : Suppose the greatest common divisor of x and y, x > y ≥ 1, is computed, using Euclid’s algorithm, in n steps. Then n ≤ logϕ (x √5 ), where the base of the logarithm is ϕ = (1 + √5 )/2, the golden ratio. The value of n is maximised when y and x are consecutive Fibonacci numbers, Fn−1 and Fn.

Theorem of the Day (April 30, 2025) : The Piff-Welsh Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/PiffWelsh/TotDPiffWelsh.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#141

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
The Piff-Welsh Theorem : If M is a transversal matroid and F is a field then M is representable over some finite extension of F. In particular, M is representable over fields of any characteristic.

Theorem of the Day (April 29, 2025) : Lieb’s Square Ice Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/MathPhysics/Lieb/TotDLieb.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#144
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Lieb’s Square Ice Theorem : For the graph of the n × n toroidal lattice, let fn denote the number of Eulerian orientations. Then
lim n→∞ f_n^(1/n^2) = (8 √3) / 9

Theorem of the Day (April 28, 2025) : Kuratowski’s 14-Set Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Topology/Kuratowski14/TotDKuratowski14.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#239
#mathematics #maths #math #theorem @Theoremoftheday

$Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Kuratowski’s 14-Set Theorem : Let T = (S, T ) be a topological space and for any subset X of S, denote by C(X) the complement S \X of X, and by K(X) the topological closure of X. Starting with an arbitrary subset of S , apply C and K repeatedly in any order; then the number of different sets that may be produced is at most 14.$

Theorem of the Day (April 27, 2025) : The Shoelace Formula
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/Shoelace/TotDShoelace.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#263
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
The Shoelace Formula : Suppose the n vertices of a simple polygon in the Euclidean plane are listed in counterclockwise order as (x_0, y_0), . . . , (x_n−1, y_n−1). Then the area A of the polygon may be calculated as:
A = (1/2) (x_0 y_1 − x_1 y_0 + . . . + x_n−2 y_n−1 − x_n−1 y_n−2 + x_n−1 y_0 − x_0 y_n−1) .

Theorem of the Day (April 26, 2025) : Girard’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/Girard/TotDGirard.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#37
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Girard’s Theorem : A spherical triangle on the surface of a sphere of radius r, with angles A, B and C, has area, T , given by
T = r^2 (A + B + C − (1/2)τ), where τ = 2π.

Theorem of the Day (April 25, 2025) : Binet’s Formula
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Binomial/Binet/TotDBinet.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#45

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Binet’s Formula : Let ϕ denote the golden ratio, 1/2 (1 + √5 ), whose first 100 decimal places are:
ϕ = 1.6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227052604 6281890244 9707207204 1893911374 . . .
Let (Fi)i≥0 be the Fibonacci sequence: F0 = 0, F1 = 1 and, for k ≥ 2, Fk = F(k−1) + F(k−2). Then, for n ≥ 0,
Fn = 1 / √5 (ϕ^n − (−ϕ)^(−n)) .

Theorem of the Day (April 24, 2025) : Poncelet’s Porism
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/Poncelet/TotDPoncelet.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#229

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Poncelet’s Porism : Suppose that two ellipses lie in the Euclidean plane, with one totally enclosed by the other. If a closed n-edge polygonal line may be inscribed in the outer ellipse so as to circumscribe (i.e. its edges being tangent to) the inner ellipse, then every point on the outer ellipse lies on some such closed n-edge polygonal line.

#Zoomposium with Prof. Dr. #Arieh #Ben-#Naim: “#Enchantment of #Entropy”

He assumes that we need a new basic #understanding of the #phenomenon of entropy. In Arieh's view, entropy, which originally stems from the 2nd #main #theorem of #thermodynamics, has been misused and incorrectly transferred as a #concept to other areas of #physics, #biology and everyday #life.

or: https://youtu.be/Km88EreH4A8

Theorem of the Day (April 23, 2025) : Bailey’s Theorem on Latin Squares
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Statistics/Bailey/TotDBailey.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#56
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Bailey’s Theorem on Latin Squares : Let G be a finite group and let a and b be ordered listings of the elements of G. Then the Cayley table L(a, b) is a quasi-complete Latin square if and only if a^(−1) and b are terraces for G.

Theorem of the Day (April 22, 2025) : A Theorem of Erdös and Wilson on Edge Colouring
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/ErdosWilson/TotDErdosWilson.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#117
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
A Theorem of Erdös and Wilson on Edge Colouring : Almost all graphs have edge-chromatic number equal to their maximum degree.

#Zoomposium with Prof. Dr. #Arieh #Ben-#Naim: “#Enchantment of #Entropy”

He assumes that we need a new basic #understanding of the #phenomenon of entropy. In Arieh's view, entropy, which originally stems from the 2nd #main #theorem of #thermodynamics, has been misused and incorrectly transferred as a #concept to other areas of #physics, #biology and everyday #life.