isaac cohen

[Johnny Midnight ⚡️ @its_The_Dr]

He wakes them up at 6 am daily! 😂

[El Jardín de Charles @CRCiencia]

El pudu es el cérvido más pequeño del mundo, natural de la región andina suramericana

[Matheorems @matheorems]

L'Hospital's Rule: Zoom In Until 0/0 Becomes Two Straight Lines

f(x) = sin(pi(x - 1)) and g(x) = ln x both hit zero at x = 1, so f(x)/g(x) there is 0/0.

Zoom in on that point. The closer you look, the straighter both curves get, until they are just their tangent lines: f rises pi for every step dx, g rises 1. Over the same dx the two heights are df(a) = pi dx and dg(a) = 1 dx, and dx cancels:

lim f(x)/g(x) = lim (df/dx)/(dg/dx) = lim f'(x)/g'(x) = pi / 1 = pi

The live ratio f(x)/g(x) closes in on 3.1416 as x slides toward 1 from both sides.

[上木 敬士郎 / Keishiro Ueki @KeishiroUeki]

立方八面体のJitter bug

[cats with jobs 🛠 @CatWorkers]

This is my mechanic. How much trouble am I in?

📸 @NornQueenKya

[Mathematica @mathemetica]

Why can grids of numbers recognize faces, recommend videos, and generate language?

Vectors hold data. Matrices transform it. Their product chains transformations. Eigenvalues show principal directions. SVD factors matrices to compress and denoise.

This math powers neural nets, dimensionality reduction, and nearly all modern AI.

The geometry of data is the geometry of intelligence.

[cats with jobs 🛠 @CatWorkers]

Greeter.

📹 meow․in․hk

[Raghu @IndiaTales7]

An educated mother, teaching her little one the ways of the world! 🐘

[Black Hole @konstructivizm]

Mars...
Now...

[The Universe @world_thingss]

A stunning view of night on Mars planet😮

[Nature Unedited @NatureUnedited]

This kangaroo pretends to faint just to get food from people

[Pulse Of Nature @_PulseOfNature]

The beginning of a new friendship.❤️

[The Universe @world_thingss]

Actual footage from MARS right now, 225 million miles away.

[Cincinnati Zoo @CincinnatiZoo]

Tucker’s favorite treat: pumpkin! 🎃

[Nature Unedited @NatureUnedited]

A royal penguin in an inspection tour with his son

[US Homeland Security News @defense_civil25]

🚨Alert: The War Department is preparing America’s military bases for a war that reaches the homeland!!

Under an operation called FORTRESS America, every major U.S. base must be able to keep operating for at least 90 days without outside power, fuel, water or supplies. Fox News Digital first reported the details!

The operation calls for portable nuclear generators, large-scale battery storage and microgrids to keep bases running when the civilian grid goes down. It also calls for stockpiles of munitions, fuel, critical minerals and medical supplies, plus backup supply chains for key defense needs!

“Power is combat now,” War Department spokesman General Sean Parnell said. He warned that global supply chains “will break” in a major war!!

Secretary of War Pete Hegseth launched the operation in a September 30 order. Parnell described it as an insurance policy for the homeland!!

America will be ready for war on its own soil!!

[isaac cohen @90c32caf4746435]

@JLozanoA 2927?

[Mathematica @mathemetica]

The Heisenberg group’s non-commutativity is already latent in ordinary matrix multiplication.

Each element (x, y, z) is sent to the upper-triangular matrix

1 z x
0 1 y
0 0 1

When two such matrices are multiplied, the product automatically inserts the correct central cross term. No extra rule is required; the group law is carried by the arithmetic itself.

The entire non-abelian structure lives inside the multiplication table of 3×3 arrays.