~~{{{{the lines in the sand}}}}/~~{{{{the lines in the sand}}}}/ ~~{{{{the lines in the sand}}}}/

The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.

Detail of a scene in the bowl of the letter 'P' with a woman with a set-square and dividers; using a compass to measure distances on a diagram. In her left hand she holds a square, an implement for testing or drawing right angles. She is watched by a group of students. In the Middle Ages, it is unusual to see women represented as teachers, in particular when the students appear to be monks. She is most likely the personification of Geometry, based on Martianus Capella's famous book De Nuptiis Philologiae et Mercurii, [5th c.] a standard source for allegorical imagery of the seven liberal arts. Illustration at the beginning of Euclid's Elementa, in the translation attributed to Adelard of Bath.

Detail of a scene in the bowl of the letter 'P' with a woman with a set-square and dividers; using a compass to measure distances on a diagram. In her left hand she holds a square, an implement for testing or drawing right angles. She is watched by a group of students. In the Middle Ages, it is unusual to see women represented as teachers, in particular when the students appear to be monks. She is most likely the personification of Geometry, based on Martianus Capella's famous book De Nuptiis Philologiae et Mercurii, [5th c.] a standard source for allegorical imagery of the seven liberal arts. Illustration at the beginning of Euclid's Elementa, in the translation attributed to Adelard of Bath.

Magnetohydrodynamics (MHD; also magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, salt water, and electrolytes. The word "magneto­hydro­dynamics" is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén,^[1] for which he received the Nobel Prize in Physics in 1970.

The fundamental concept behind MHD is that magnetic fields can induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electro­magnetism. These differential equations must be solved simultaneously, either analytically or numerically.

Now call me naive but last time I looked which is now water is down as

1. the most abudant pile of stuff

2. pretty much everywhere

3. most of every hominid

4. wet

5. the best conductor of electricity

<<== this thing is acting surprised that water conducts electricity

that is surprising

and

not surprising

at the same time

like a famous dead cat

onward to the torioidal toroids

Uppercase Pi[edit]

The uppercase letter Π is used as a symbol for:

• In textual criticism, Codex Petropolitanus, a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia.

• In legal shorthand, it represents a plaintiff.

In science and engineering:

• The product operator in mathematics, indicated with capital pi notation Π (in analogy to the use of the capital Sigma Σ as summation symbol).

• The osmotic pressure in chemistry.

• The viscous stress tensor in continuum mechanics and fluid dynamics.

Lowercase Pi[edit]

The lowercase letter π is used as a symbol for:

• The mathematical real transcendental (and thus irrational) constant π ≈ 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter "π" is the first letter of the Greek words περιφέρεια 'periphery', π is used is math, and περίμετρος 'perimeter', i.e. the circumference.

• The prime-counting function in mathematics.

• Homotopy groups in algebraic topology.

• Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.

• The hadron called the pion (pi meson).

• Economic profit in microeconomics.

• Inflation rate in macroeconomics.

• A type of chemical bond in which the p orbitals overlap, called a pi bond.

• The natural projection on the tangent bundle on a manifold.

• The unary operation of projection in relational algebra.

• Policy in reinforcement learning.

• Polyamory^[1]

History[edit]

An early form of pi was , appearing almost like a gamma with a hook.

Variant pi[edit]

Variant pi or "pomega" (

{\displaystyle \varpi \,\!}

or ϖ) is a glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It was also used in the minuscule script. It is a symbol for:

• Angular frequency of a wave in fluid dynamics (angular frequency is usually represented by

• {\displaystyle \omega }

• but this may be confused with vorticity in a fluid dynamics context).

• Longitude of pericenter in celestial mechanics.^[2]

• Comoving distance in cosmology.^[3]

• Single-scattering albedo in radiative transfer.

• Mean fitness of a population in biology.

• Fundamental weights of a representation (probably to better distinguish from elements

• {\displaystyle w}

• of the Weyl group, than the usual notation

• {\displaystyle \omega }

• ).

• The lemniscate constant.^[4]