Minimal Surface

9

The Most Beautiful Mathematical Equations.

1. General Relativity

The equation above was formulated by Einstein as part of his groundbreaking general theory of relativity in 1915. The theory revolutionized how scientists understood gravity by describing the force as a warping of the fabric of space and time. The right-hand side of this equation describes the energy contents of our universe (including the ‘dark energy’ that propels the current cosmic acceleration). The left-hand side describes the geometry of space-time. The equality reflects the fact that in Einstein’s general relativity, mass and energy determine the geometry, and concomitantly the curvature, which is a manifestation of what we call gravity.

2. Standard Model
This equation describes the collection of fundamental particles currently thought to make up our universe. It has successfully described all elementary particles and forces that we’ve observed in the laboratory to date - except gravity, including recently discovered Higgs boson and phi in the formula. It is fully self-consistent with quantum mechanics and special relativity.

3. The Fundamental Theorem of Calculus 
This equation forms the backbone of the mathematical method known as calculus, and links its two main ideas, the concept of the integral and the concept of the derivative. It allows us to determine the net change over an interval based on the rate of change over the entire interval. The seeds of calculus began in ancient times, but much of it was put together in the 17th century by Isaac Newton, who used calculus to describe the motions of the planets around the sun.

4. 1 = 0.999999999….
This simple equation states that the quantity 0.999 followed by an infinite string of nines is equivalent to one, and is made by mathematician Steven Strogatz of Cornell University. Many people don’t believe it could be true. It’s also beautifully balanced. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity.

5. Special Relativity
Einstein makes the list again with his formulas for special relativity, which describes how time and space aren’t absolute concepts, but rather are relative depending on the speed of the observer. It shows how time dilates, or slows down, the faster a person is moving in any direction.

6. Euler’s Equation
This simple formula encapsulates something pure about the nature of spheres. It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces, E the number of edges and V the number of vertices, you will always get V – E + F = 2. So, for example, take a tetrahedron, consisting of four triangles, six edges and four vertices. If you blew hard into a tetrahedron with flexible faces, you could round it off into a sphere, so in that sense, a sphere can be cut into four faces, six edges and four vertices. And we see that V – E + F = 2. Same holds for a pyramid with five faces - four triangular, and one square - eight edges and five vertices, and any other combination of faces, edges and vertices. The combinatorics of the vertices, edges and faces is capturing something very fundamental about the shape of a sphere.

7. Euler–Lagrange Equations and Noether’s Theorem
In this equation, L stands for the Lagrangian, which is a measure of energy in a physical system, such as springs, or levers or fundamental particles. Solving this equation tells you how the system will evolve with time. A spinoff of the Lagrangian equation is called Noether’s theorem. Informally, the theorem is that if your system has a symmetry, then there is a corresponding conservation law. For example, the idea that the fundamental laws of physics are the same today as tomorrow (time symmetry) implies that energy is conserved. The idea that the laws of physics are the same here as they are in outer space implies that momentum is conserved. 

8. The Callan-Symanzik Equation
Basic physics tells us that the gravitational force, and the electrical force, between two objects is proportional to the inverse of the distance between them squared. However, tiny quantum fluctuations can slightly alter a force’s dependence on distance, which has dramatic consequences for the strong nuclear force. What the Callan-Symanzik equation does is relate this dramatic and difficult-to-calculate effect, important when the distance is roughly the size of a proton, to more subtle but easier-to-calculate effects that can be measured when the distance is much smaller than a proton.

9. The Minimal Surface Equation
The minimal surface equation somehow encodes the beautiful soap films that form on wire boundaries when you dip them in soapy water. The fact that the equation is 'nonlinear,’ involving powers and products of derivatives, is the coded mathematical hint for the surprising behavior of soap films. 

the signs as starter pokemon

ARIES- Charmander- The flame that burns at the tip of its tail is an indication of its emotions. The flame wavers when Charmander is happy, and blazes when it is enraged.

TAURUS- Bulbasaur- Bulbasaur can be seen napping in bright sunlight. There is a seed on its back. By soaking up the sun’s rays, the seed grows progressively larger.

GEMINI- Piplup- Because it is very proud, it hates accepting food from people. Its thick fur guards it from cold.

CANCER- Squirtle- Squirtle’s shell is not merely used for protection. The shell’s rounded shape and the grooves on its surface help minimize resistance in water, enabling this Pokémon to swim at high speeds.

LEO-Chimchar- Its fiery rear end is fueled by gas made in its belly. Even rain can’t extinguish the fire.

VIRGO- Chikorita- A sweet aroma gently wafts from the leaf on its head. It is docile and loves to soak up sun rays.

LIBRA- Mudkip- The fin on Mudkip’s head acts as highly sensitive radar. Using this fin to sense movements of water and air, this Pokémon can determine what is taking place around it without using its eyes.

SCORPIO- Totodile- Despite the smallness of its body, Totodile’s jaws are very powerful. While the Pokémon may think it is just playfully nipping, its bite has enough power to cause serious injury.

SAGITTARIUS- Torchic- Torchic has a place inside its body where it keeps its flame. Give it a hug—it will be glowing with warmth. This Pokémon is covered all over by a fluffy coat of fur.

CAPRICORN- Turtwig- It undertakes photosynthesis with its body, making oxygen. The leaf on its head wilts if it is thirsty.

AQUARIUS- Treecko- Treecko is cool, calm, and collected—it never panics under any situation. If a bigger foe were to glare at this Pokémon, it would glare right back without conceding an inch of ground.

PISCES- Froakie- It protects its skin by covering its body in delicate bubbles. Beneath its happy-go-lucky air, it keeps a watchful eye on its surroundings.

2

Pata (gauntlet-sword)

This uniquely Indian form of sword combined weapon and armor. The pata was gripped by the crossbar inside the hilt, with the blade extending as a projection of the forearm.

As European traders came to India in the 1500s and 1600s, they brought swords from the blademaking centers in Spain, Italy, and Germany. The blades of these swords were much admired in India, and some were fitted into Indian-made hilts. English swords were less respected: one Indian admiral of the 1600s remarked that English blades were “only fit to cut butter.”

These two pieces are exquisite examples of the decorative styles of northern and southern India. The gilded pata is decorated using the characteristic “koftgari” technique of Mughal northern India, which was heavily influenced by the cultural traditions of Persia. The gold and silver inlay is incised with fine decorative details visible only under the closest scrutiny. The south Indian pata has minimal surface decoration, relying instead on the sculptural form of the metal itself for visual effect.

Description

Long, double-edged steel European blade with spatulate point. Riveted at the base of the blade is a gauntlet-like defense that is globose at the hand, fitted within with a crossbar grip. The deep gutter-like extension over the wrist and lower forearm is open on the inside, and fitted with a thin, textile lining, and expands towards the opening for the arm. There is a pivoting cross-brace near the opening at the top. The edge here is pointed, and with a boxed turn. The surface and edges are decorated with foliate motifs in both gold and silver “koft-gari” bands; the surface of the gold is incised with fine decorative detail.

Curator’s Comments

This uniquely Indian form of sword combined weapon and armor. The pata was capable of powerful cuts in virtually any direction. Since its use required special training and skill, patas were often part of swordplay demonstrations. There are even references to warriors with patas in both hands, appearing “much like a windmill.” This exquisite piece is decorated in the characteristic “koftgari” technique of Mughal-period arms and armor, with surface inlay of gold and silver, the precious metal incised with fine decorative details visible only under the closest scrutiny. [India Exhibition]