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**Paysages Mathématiques** @paysmaths@mathstodon.xyz · 7h

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (April 18, 2025) : The Polygonal Number Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/NumberTheory/Eureka/TotDEureka.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#262

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
The Polygonal Number Theorem : For any integer m > 1, every non-negative integer n is a sum of m + 2 polygonal numbers of order m + 2.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · 2d

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (April 16, 2025) : Karp’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/LogicAndComputerScience/VCNPC/TotDVCNPC.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#187
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Karp’s Theorem (Detail) : Vertex Cover is NP-Complete.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Apr 6

Apr 6

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (April 6, 2025) : The Lucas-Lehmer Test
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/NumberTheory/LucasLehmer/TotDLucas.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#127
#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
The Lucas-Lehmer Test : The number Mp = 2^p − 1, for p an odd prime, is itself prime if and only if it divides Sp−1, the (p − 1)-th term in the series: S1 = 4, S2 = 14, . . . , and, for i ≥ 1, Si+1 = Si^2 − 2.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Apr 3

Apr 3

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (April 3, 2025) : Noether’s Symmetry Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/MathPhysics/Noether/TotDNoether.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#86

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Noether’s Symmetry Theorem : Suppose a system of particles in classical mechanics exhibits some symmetry, i.e. its Lagrangian, L , is invariant under changes to some variable s, so that ∂L/∂s = 0. Then there is some associated property C of the system which is conserved: dC/dt = 0.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 28

Mar 28

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 28, 2025) : The Sophomore’s Dream
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Analysis/Sophomore/TotDSophomore.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#147

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : The Sophomore’s Dream.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 27

Mar 27

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 27, 2025) : Bézout’s Identity
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/NumberTheory/BezoutId/TotDBezoutId.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#249

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Bézout’s Identity : Let a and b be positive integers with greatest common divisor equal to d. Then there are integers u and v such that au + bv = d.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 19

Mar 19

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 19, 2025) : Archimedes’ Equiareal Map Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/Archimedes/TotDArchimedes.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#181

$Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Archimedes’ Equiareal Map Theorem : Let S be the unit sphere defined relative to the x, y and z axes by x^2 + y^2 + z^2 = 1 and let S′ be the bounding cylinder defined by x^2 + y^2 = 1. Let f be the map f : (x, y, z) → (x / √(x^2 + y^2) , y / √(x^2 + y^2) , z) from S \{(0, 0, 1), (0, 0, −1)} to S ′ which takes a point P on the sphere having height zP, |zP| < 1, to the nearest point on the cylinder which has height zP and which is collinear with P and (0, 0, zP). Then f is an equiareal diffeomorphism.$

#mathematics #maths #math

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 14

Mar 14

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 14, 2025) : The Circle Area Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/CircleArea/TotDCircleArea.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#233

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
The Circle Area Theorem : The area of a circle of radius r and circumference C is identical to that of a right triangle of height r and base C.

#mathematics #maths #math

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 7

Mar 7

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 7, 2025) : Wagner’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/Wagner/TotDWagner.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#25
#mathematics #maths #math #theorem

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.
Wagner’s Theorem : A graph G is planar if and only if it contains neither K5 nor K3,3 as a graph minor.

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Mar 5

Mar 5

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (March 5, 2025) : The Diaconis–Holmes–Montgomery Coin Tossing Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/MathPhysics/Cointossing/TotDCoinTossing.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#164

Comprehensive presentation of the "Theorem of the Day" : The Diaconis–Holmes–Montgomery Coin Tossing Theorem.

#mathematics #maths #math

**The Krononaut Moon Project** @KronoMoon@me.dm · Feb 24 *

Feb 24 *

The Krononaut Moon Project @KronoMoon@me.dm

The Amazing History of #Locality in #Theoretical #Physics

#Philosopher #DavidAlbert rambles (his word) for ½ hour on the often gripping (and #funny) #saga of #nonlocality in #scientific #thought. Starting with #fish, he ushers us along to #Bell's #Theorem in the 1960s. It seems we are "inescapably" in the age of nonlocality. Perhaps an age of #TimeTravelers?

https://www.youtube.com/watch?v=y_GM12xjBWY 2023 Oct 25
https://en.wikipedia.org/wiki/Bell%27s_theorem

YouTubeThe Amazing History of Locality in Theoretical Physics | David AlbertBy Robinson's Podcast Clips

#Community #TimeTravel #Research

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Feb 23

Feb 23

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (February 23, 2025) : Euclid’s Pythagorean Formula
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/EuclidsPythagorean/TotDEuclidsPythagorean.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#261

#mathematics #maths #math

**Paysages Mathématiques** @paysmaths@mathstodon.xyz · Feb 16

Feb 16

Paysages Mathématiques @paysmaths@mathstodon.xyz

Theorem of the Day (February 16, 2025) : Heath’s Finitely Discontinuous Function Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Topology/Heath/TotDHeath.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#162
#mathematics #maths #math #theorem

**The Krononaut Moon Project** @KronoMoon@me.dm · Feb 9 *

Feb 9 *

The Krononaut Moon Project @KronoMoon@me.dm

How Noether’s Theorem Revolutionized Physics

❛❛ Emmy #Noether showed that #fundamental #physical #laws are just a consequence of simple #symmetries. A #century later, #her insights continue to shape #physics. ❜❜