Tensors encode multilinear maps on a vector space as single algebraic objects that remain unchanged under any basis switch. Rank-0 tensors are scalars, rank-1 are vectors. A rank-2 case is the matrix
P = ⎡Pₓₓ Pₓᵧ Pₓ𝓏⎤
⎢Pᵧₓ Pᵧᵧ Pᵧ𝓏⎥
⎣P𝓏ₓ P𝓏ᵧ P𝓏𝓏⎦
whose nine entries give the force-per-area vectors on the six faces of a material cube. Rank equals the number of indices; a rank-3 tensor in three dimensions therefore stores exactly 3³ = 27 components.
Finite-element codes for turbine blades feed the Cauchy stress tensor into the equilibrium equations to compute local strain and remaining fatigue life under cyclic centrifugal loads.
Pick any labeled point on the black Mandelbrot set and the connected image shows the Julia set for that exact complex number c.
Both sets come from the same recurrence zₙ₊₁ = zₙ² + c. The Mandelbrot records every c where the sequence starting at 0 stays bounded; each Julia records every starting z that stays bounded for one fixed c. The six examples illustrate the dramatic shape changes across the parameter plane.
Film studios run these iterations on GPUs to synthesize endless fractal detail in digital landscapes for movies.
Une riche collection d’antiquités égyptiennes, 2600 pièces exposées dans neuf salles.
📸 « Modèle » déposé dans une tombe qui permet au défunt de restituer son cadre domestique dans l’au-delà. Ici, scène de vêlage.
📍Musée des Beaux-Arts de Lyon 🇫🇷
This video presents the complete Trigonometric Unit Circle with all important standard angles, exact radian measures, degree values, sine values, cosine values, coordinate relationships, and mathematical patterns used in school mathematics, competitive examinations,
The interior of the Sagrada Família is composed of precisely 52 stone pillars, representing the 52 Sundays of the liturgical year, a reminder of what Antoni Gaudí believed to be the foundation of the Christian life: faithful, week-by-week worship centered on the Eucharist.
Visualization of the continuity equation.
Showing how any change in mass density inside a fixed control volume is exactly balanced by the net mass flux through its boundary. Blue particle concentration represents, the green arrow represents velocity, and the orange arrows show mass entering and leaving. The density is redistributed, but no mass is created or destroyed.
An 1875 drawing of St. Paul's Cathedral in London, built by Christopher Wren from 1675 to 1710. Look at the cut-through on the top left. The dome is really three domes. The one you see inside is painted like heaven. The big one you see from the street is just timber and lead, built for looks. Hidden between them is a brick cone, and that's the part actually holding up the 850-ton stone lantern on top.