Physical world and mathematics

Penrose process

The Penrose process, or Penrose mechanism, is a method proposed by Roger Penrose in 1969 for extracting rotational energy from a rotating Kerr black hole.

Penrose stairs

The Penrose stairs, also called the impossible staircase, form a two-dimensional illusion of steps that loop forever while always ascending, published by Lionel and Roger Penrose in 1958.

Penrose tiling

The Penrose tiling, also known as Penrose tiles, is a nonperiodic tiling of the plane found by Roger Penrose in 1974, built from two tiles with matching rules.

The Penrose transform is an integral-geometric transform, introduced by Roger Penrose in his twistor theory, that converts complex-analytic data on twistor space into solutions of massless free-field equations on spacetime.

Penrose triangle

The Penrose triangle, or Penrose tribar, is an impossible figure of three beams meeting at right angles, drawn by Reutersvärd in 1934 and published by the Penroses in 1958.

Penrose–Hawking singularity theorems

The Penrose–Hawking singularity theorems are results in general relativity proving singularities, notably Penrose's 1965 theorem on gravitational collapse, which earned him half of the 2020 Nobel Prize in Physics.

Penta-graphene

Penta-graphene is a theoretically proposed two-dimensional carbon allotrope, predicted in 2015, built entirely from carbon pentagons rather than hexagons; it remains unsynthesized and disputed as experimentally attainable.

Pentaborane(9)

Pentaborane(9) (B₅H₉) is a colorless, volatile boron hydride liquid with a square-pyramidal structure, first reported in 1923 and studied as a high-energy jet fuel until toxicity and boron oxide deposits ended that use.

Pentabromodiphenyl ether

Pentabromodiphenyl ether (pentaBDE) is a brominated flame retardant, the main component of a commercial mixture used in polyurethane foam in furniture and mattresses before its phase-out in 2004.

Pentabromopseudilin

Pentabromopseudilin (PBP, PBrP) is a heavily brominated antibiotic made by marine bacteria such as Pseudoalteromonas, first described in 1966; it kills Gram-positive bacteria by dissipating their proton motive force.

Pentacene

Pentacene is a polycyclic aromatic hydrocarbon of five linearly fused benzene rings, a benchmark p-type organic semiconductor used in field-effect transistors and singlet fission solar cells, discovered in 1912.

Pentacene-doped p-terphenyl

Pentacene-doped p-terphenyl is an organic host-guest crystal, pentacene molecules dispersed at low concentration in a p-terphenyl lattice, used for single-molecule spectroscopy, zero-field room-temperature masing, and pressure and temperature sensing.

Pentachlorophenol

Pentachlorophenol (PCP) is a manufactured organochlorine compound used since 1936 as a heavy-duty wood preservative, mainly for utility poles; the EPA classified it as carcinogenic to humans and is phasing it out by 2027.

Pentaerythritol

Pentaerythritol, also known as monopentaerythritol, is a white crystalline four-hydroxyl alcohol (C₅H₁₂O₄) made from formaldehyde and acetaldehyde and used mainly in alkyd resins and the explosive PETN.

Pentaerythritol tetranitrate

Pentaerythritol tetranitrate (PETN), also known as nitropenta, is the nitrate ester of pentaerythritol, a white crystalline solid used as a powerful explosive and as a vasodilator drug for angina.

Pentafoil knot

The pentafoil knot (cinquefoil knot, Solomon's seal knot) is the simplest torus knot after the trefoil, with five crossings, first made as a 160-atom molecule in 2011.

Pentagastrin

Pentagastrin is a synthetic pentapeptide analog of the hormone gastrin, used chiefly as a diagnostic stimulant in gastric acid secretion testing and the calcitonin test for medullary thyroid carcinoma.

Pentagon

A pentagon is a polygon with five straight sides forming a closed shape; each interior angle of a regular pentagon is 108°, and its diagonal-to-side ratio is the golden ratio.

Pentagonal number theorem

The pentagonal number theorem is an identity of Leonhard Euler stating that ∏(1 − x^m) equals a series with generalized pentagonal-number exponents, underlying his recurrence for the partition function.

Pentagram

A pentagram, also called a pentacle or pentalpha, is a five-pointed star polygon {5/2} whose points each measure 36 degrees and which is filled with golden-ratio proportions.

Pentalayer graphene

Pentalayer graphene is a stack of five single-atom-thick carbon sheets whose properties depend on stacking; its rhombohedral form hosts superconductivity, magnetism, and quantum anomalous Hall effects.

Pentalene

Pentalene is a bicyclic hydrocarbon, C₈H₆, made of two fused five-membered carbon rings and known as the archetypal antiaromatic hydrocarbon, so reactive it dimerizes above −196 °C.

Pentane

Pentane, also called amyl hydride, is a flammable liquid alkane, C5H12, from natural gas and crude oil, used as a laboratory solvent and foam blowing agent.

Pentaprism

A pentaprism is a five-sided glass prism that bends light by exactly 90° regardless of the entry angle, used in surveying instruments, optical metrology, and SLR viewfinders.

Pentaquark

A pentaquark is an exotic hadron made of four quarks and one antiquark, first confirmed by CERN's LHCb experiment in 2015 and long predicted by the quark model.

Pentazenium

Pentazenium (N5+) is a five-nitrogen cation first prepared in 1999, one of only three known homoleptic polynitrogen species and studied as a high energy density material.

Pentazolate

Pentazolate (cyclo-N5−) is an aromatic anion of a five-membered ring of only nitrogen atoms, first isolated as a stable salt in 2017 and studied for high-energy-density materials.

Pentetic acid

Pentetic acid, also called diethylenetriaminepentaacetic acid (DTPA), is a synthetic polyaminopolycarboxylic acid that strongly binds metal ions; its calcium and zinc salts are FDA-approved chelating agents for plutonium contamination.

Pentlandite

Pentlandite is a bronze-yellow iron-nickel sulfide mineral, (Fe,Ni)₉S₈, and the most important ore of nickel, mined at Sudbury and associated with pyrrhotite in ultramafic igneous rocks.