⟨😺|Federico⟩

Física y matemáticas. Socialdemocracia. A favor de la ciencia. En oposición a la posmodernidad. Siempre aprendiendo algo nuevo. Catlover. 🐈🇲🇽

[⟨😺|Federico⟩ @diff_form]

Soy el hombre más suertudo del mundo por tenerte de novia... @Itsmesweets1 🥺😭❤️

[Father Alchemist @PadreHomunculo3]

Me veo en la necesidad de postear esta escena de Looney Tunes: De nuevo en acción por alguna razon xdddddddd

[⟨😺|Federico⟩ @diff_form]

@TendenciasMX Por eso la dejó el Nodal (?)

[Lugar Cinema🎬 @LugarCinema]

Tim Burton no estaba convencido de incluir en Beetlejuice (1998) la escena de ‘Day-O’ ya que pensaba que no era muy divertida y que no gustaría al público.

Pero había un factor clave: CATHERINE O'HARA

La escena acabaría convirtiéndose en una de las más icónicas de la película.

[ScieVision @scievision369]

Frenet-Serret Formulas ✍️

Imagine you are driving a car along a winding mountain road that curves and twists through three-dimensional space like a roller coaster. At every moment on this path, you sense three distinct directions. There is the direction straight ahead, which indicates where the road is currently taking you. There is also the direction toward the inside of the curve you are navigating, the direction you would lean into while turning. Finally, there is the direction perpendicular to the road surface beneath you, pointing straight up from the curve. These three directions together define your complete orientation at each moment. As you travel, all three directions shift and rotate to reflect the changing geometry of the path. The Frenet-Serret formulas provide a precise mathematical description of how and why these three directions change as you move along any curved path in three-dimensional space.

The core of this framework is a natural way to measure your position along the curve called arc length. This is simply the actual distance you have traveled along the curve from a fixed starting point. For example, if you have walked three meters along the curve from the starting point, your position is labeled three. This method of labeling points on a curve is the most natural and meaningful, as it relies solely on the shape of the curve itself, not on how fast someone is moving. The diagram shows two nearby points on the curve marked by their arc length positions, with the position vector r pointing to each point in three-dimensional space and a small arc length distance separating them.

At every point on the curve, the Frenet-Serret framework identifies three special directions that together form a moving coordinate system, known as the Frenet frame. This frame travels along the curve and constantly adjusts to its local geometry. The first direction is the tangent vector, represented by the green arrow labeled T in the diagram. This vector points straight ahead in the direction the curve is heading at that moment, similar to the direction you face when walking along a path. It always has a length of one, capturing only direction, not speed. The second direction is the normal vector, indicated by the red arrow labeled N in the diagram. This vector points toward the inside of the bend, toward the center of curvature, and is perpendicular to the tangent vector. It arises naturally as the tangent vector changes direction by rotating. The direction it rotates toward is exactly the normal direction. The third direction is the binormal vector, shown as the purple arrow labeled B in the diagram. This vector is perpendicular to both the tangent and normal vectors, pointing straight out of the plane defined by the other two vectors. For a curve lying flat in a plane, like a circle, the binormal vector always points in the same fixed direction. However, for a curve spiraling through three-dimensional space, like a helix, the binormal vector continuously rotates as you travel along the curve. All three vectors are always mutually perpendicular, each with a length of one, forming a perfect three-dimensiona coordinate system customized to the local geometry of the curve, as illustrated in the diagram where you can see all three arrows at each point sticking out at right angles.

The two key numbers that characterize the geometry of a curve are curvature and torsion. Curvature, labeled kappa in the diagram, measures how sharply the curve bends at each point. A straight line has zero curvature because the direction of travel never changes. A large gentle circle has small curvature, while a tight sharp loop has large curvature. Curvature is always greater than or equal to zero and indicates the rate at which the tangent vector rotates as you move along the curve. The faster the direction of travel changes, the higher the curvature.

[⟨😺|Federico⟩ @diff_form]

@ArrepentidosLLA ¿Cuánto a que lo reeligen?

[⟨😺|Federico⟩ @diff_form]

@MarxArriaga Ya, ya cálmate, wey, ni que fueras la gran cosa, mucho menos tus libros.

[Cosmos Archive @cosmosarcive]

Torque is what makes a force create rotation, and it depends on three things: the force you apply, the distance from the pivot, and the angle between them. Push farther from the pivot and as close to 90° as possible for the greatest turning effect.

A simple idea that explains everything from tightening a bolt to how engines, gears, and machines work.

[⟨😺|Federico⟩ @diff_form]

@SomosMxMexico @azucenau @Amadoelquelolea @beltrandelrio @CarlosLoret @El_Universal_Mx @laoctavadigital @LuisCardenasMx @Radio_Formula @Reforma @acostanaranjo Pues si empezamos defendiendo presuntos criminales, no creo que nos vaya muy bien en el futuro...

[Cliff Pickover @pickover]

Mathematics and beauty.

"It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions."

By Ben Bartlett, @bencbartlett, Used with permission.

[Philosophy Of Physics @PhilosophyOfPhy]

When Albert Einstein completed general relativity in November 1915, he had produced a new theory of gravity but its nonlinear field equations were extremely difficult to solve exactly.

Only weeks later, while serving on the Russian front during the First World War, German astronomer Karl Schwarzschild found the first non-trivial exact solution. It described the gravitational field in the empty space outside a perfectly spherical, non-rotating mass. Einstein presented Schwarzschild’s paper to the Prussian Academy in January 1916.

The Schwarzschild metric is not merely a formula for gravitational force. It describes the geometry of spacetime itself: how clocks run, how radial distances are measured, and how particles and light move around a spherical mass.

Far from the object, spacetime approaches the nearly flat geometry of special relativity. Closer to it, gravitational time dilation becomes stronger and trajectories depart increasingly from Newtonian predictions.

The expression also contains the radius

rₛ = 2GM/c²

now called the Schwarzschild radius. For an ordinary star or planet, this radius lies deep inside the object. But when matter is compressed within it, the radius becomes an event horizon, the boundary of a non-rotating black hole.

The apparent breakdown of the displayed coordinates at this radius is not a physical tear in spacetime; it is a coordinate singularity.

Its importance extends far beyond black holes. The Schwarzschild geometry provides the basic framework for calculating gravitational redshift, light bending, planetary orbits, Mercury’s perihelion advance and the motion of matter near compact objects.

Real astronomical black holes often rotate and require the more general Kerr metric, but the Schwarzschild solution remains the simplest laboratory for understanding how gravity becomes geometry and how Einstein’s equations transformed black holes from mathematical possibilities into physical objects.

[Mathematica @mathemetica]

Bernhard Riemann introduced the metric tensor to quantify distances and angles in curved spaces.

The equation is ds² = ∑ gᵢⱼ dxⁱ dxʲ where ds² is the infinitesimal squared distance, gᵢⱼ the metric tensor components and dxⁱ the coordinate differentials. It extends the dot product idea to Riemannian manifolds and equals the Kronecker delta in flat space but changes with position in curved space. This is essential for general relativity.

It is used to determine spacetime curvature effects on satellite orbits and light propagation in astronomy.

[⟨😺|Federico⟩ @diff_form]

@jorgegogdl Lo dice un wey que ni una pinche suma de polinomios sabe hacer...

[Philosophy Of Physics @PhilosophyOfPhy]

In 1918, German mathematician Emmy Noether published one of the deepest results in theoretical physics.

While studying the mathematical structure of general relativity, she proved that every continuous symmetry of a physical system corresponds to a conservation law.

If the laws of physics do not change with time, energy is conserved. If they do not change from one place to another, momentum is conserved. If they are unchanged by rotation, angular momentum is conserved.

Noether’s theorem transformed conservation laws from separate experimental rules into consequences of symmetry. It now sits at the foundation of classical mechanics, quantum field theory, particle physics and general relativity.

Modern physics does not merely ask what quantities are conserved; it asks what symmetry of nature makes that conservation inevitable.

[⟨😺|Federico⟩ @diff_form]

@guruchuirer ¿Lo dicen porque en Polanco los meseros son argentinos? :o

[⟨😺|Federico⟩ @diff_form]

Lo peor es que siga siendo presidente con todo eso encima... Los gringos son un asco.

[Apu @Apu_elrojo]

Donald Trump ha sido condenado a pagar 5,8 millones de dólares por violar a una mujer y no ha sido ni tendencia en Twitter.

[Kev Cuev @kevcuev]

Para qué quieren las Malvinas? Para dárselas también a Israel?

[⟨😺|Federico⟩ @diff_form]

@VentaneandoUno Comunicado vacío. Pedro Sola se seguirá enriqueciendo diciendo pendejadas de forma impune.

[⟨😺|Federico⟩ @diff_form]

@USAmbMex @POTUS @realDonaldTrump Si tuvieran compromiso con ello, dejarían de mandar armas, harían algo contra su red de distribución interna y, mejor aún, ya pondrían atención a sus pinches ciudadanos todos drogos que son los que provocan la demanda por tanta puta porquería. Esto sólo es politiquería barata.

[Jay Cummings @LongFormMath]

Emmy Noether