Eduardo Requena

Matemáticas UCV.

[Mathematica @mathemetica]

A point fixed on a circle rolling inside a larger fixed circle traces a hypotrochoid.

Shown here with parameters (a, b, h) where a = 1 is the fixed radius, b the rolling radius and h the distance from the rolling center to the tracing point.
The equations are
x = (a − b) cos t + h cos(((a − b)/b) t)
y = (a − b) sin t − h sin(((a − b)/b) t).
Varying the ratios of b and h produces rings, multi-lobed flowers, sharp stars and rounded polygons.
Spirograph drawing sets generate these patterns through interlocking plastic disks.

[Dani Lerer @danilerer]

Aplauso, medalla y beso para @BoyGeorge, quien ha lanzado una canción en solidaridad con Israel: "WE WILL DANCE AGAIN".

Una de las primeras frases dice: "Tú dices genocidio, yo digo guerra; para eso está el ejército cuando te atacan".

[Mathematica @mathemetica]

From one icosahedron, targeted edge, face and vertex operations under icosahedral symmetry produce the complete family of related Archimedean solids:

- Dual yields the dodecahedron,
- Rectification the icosidodecahedron,
- Bitruncation the truncated dodecahedron and truncated icosahedron,
- Cantellation the rhombicosidodecahedron,
- Omnitruncation the truncated icosidodecahedron, and
- Snubbing the chiral snub dodecahedron.

These same forms model the carbon cages of fullerenes such as C₆₀ and the protein shells of icosahedral viruses.

[Mathematica @mathemetica]

Mathematicians isolate graphs with extreme traits under simple names that stick for generations. The Balaban 10-cage realizes the (3,10)-cage with 70 vertices. Errera and Kittell graphs relate to the four color theorem. The Frucht graph is the smallest 3-regular with trivial automorphism group.

Circuit designers draw on the Goldner-Harary and Wagner graphs for planar embeddings in printed circuit board layouts.

[Yisrael official 🕎 @YisraelOfficial]

💙🤍💙

Shabbat Shalom❣️

[Mathematica @mathemetica]

Prime factors of n determine how many integers below it share no common divisors with n. Euler’s formula states:

φ(n) = n ∏_{p|n} (1 − 1/p)
with the product over distinct primes p dividing n.

RSA encryption generates its public and private keys by computing this totient for the product of two large primes.

[Cliff Pickover @pickover]

DMT machine elves are entities frequently reported by individuals under the influence of the psychedelic drug N,N-dimethyltryptamine (DMT). Coined by ethnobotanist Terence McKenna, they are described as autonomous, shape-shifting, and highly intelligent beings.

[Cliff Pickover @pickover]

Math.

Thébault's theorem. Wow. Place squares on the sides of any parallelogram, and their centers will always form a square.

[SissiEmperatriz 🇮🇱 @GabyLob]

Los argentinos están perdiendo el tiempo explicándole al mundo que no son racistas.

El mismo tiempo que perdimos judíos, explicándole al mundo que no somos genocidas.

Hay una verdad incómoda: ninguna cantidad de evidencia va a convencer a un idiota.

Porque el problema nunca fue la falta de pruebas. Ellos ya decidieron quiénes somos. No para entendernos, sino para odiarnos con menos culpa.

[Eduardo Requena @elgeometra]

Shabat Shalom

[HENRY ORTIZ @henryortiztv]

Argentina no es un país racista. Es una nación noble y generosa que ha recibido con respeto y solidaridad a millones de migrantes, entre ellos miles de venezolanos. No comparto esa campaña sucia que busca desprestigiar al pueblo argentino. Desde Venezuela expresamos nuestro apoyo y respeto a nuestros hermanos argentinos.

[𝐌𝐮𝐬𝐢𝐜 - 𝐌𝐨𝐯𝐢𝐞 - 𝐀𝐧𝐝 𝐌𝐨𝐫𝐞⭐️❤️ @NgocThach74]

These two were born to sing this song together ❤️

[🌻Music 🎶🎻🎷 @khalythai]

A timeless love song that still warms the heart, with Shania Twain at her very best. ✨🎵

[iPaul @iPaulCanada]

2026世界人工智能大会，某科技公司展示的跨时代教具--AI黑板

[Irving Gatell @IrvingGatell]

Los trabajadores no generan riqueza.
Generan bienes de consumo.
Si no se venden, no sirve de nada.
La riqueza no es una cosa.
Es una dinámica.
No sé genera en la fábrica.
Se genera en el mercado.

[Mathematica @mathemetica]

Individual molecules can arrange themselves into elaborate nanoscale constructions without external direction.

Amphiphilic units featuring polar heads and nonpolar tails build up into parallel multilayered sheets, seamless cylindrical tubes, and fully enclosed spheres that incorporate triangular internal patterns.

Aggregates of simpler units tile into flat multicolored layers, wind into cylinders displaying alternating stripes, and close off into multifaceted polyhedral shells with accentuated edges. More intricate molecules bearing varied atomic centers form upright columnar piles, coiled tubular shapes, and extended cubic grids containing periodic internal markers.

These self-organized architectures find use in liposomal formulations for controlled drug release within the body.

[Mathematica @mathemetica]

Four-dimensional regular polytopes reveal complex symmetries in these multi-style projections.

Shown are the 5-cell {3,3,3}, 8-cell {4,3,3}, 16-cell {3,3,4}, 24-cell {3,4,3}, 120-cell {5,3,3} and 600-cell {3,3,5} in wireframe orthographic projections inside Petrie polygons, solid orthographic projections, Schlegel diagrams, and hyperspherical stereographic projections with noted cell- or vertex-centered orientations.

These geometric tools help roboticists simulate and optimize paths in multi-dimensional configuration spaces for complex machinery control.

[Massimo @Rainmaker1973]

Round About Four Dimensions, a tesseract kinetic sculpture by Julius von Bismarck at CERN

[Math901 @MathMath901]

#math
Kepler Triangle
Since the golden ratio satisfies φ² = φ + 1, there exists a right triangle with side lengths √φ, 1, and φ, which are in geometric progression.