Mathematics

Numeric Demonstrator', an elementary teaching aid patented by Ethel Linay in about 1900.. This elementary arithmetical teaching apparatus consists of ten wooden rods with squared paper pasted on them in order to show multiplication visually.

• 'Numeric Demonstrator', c 1900.

A single surface model made by Alan Bennett in Bedford, 1995. It consists of a sphere with three interlinked loops the equivalent of three interconnected Klein bottles. A Klein bottle has no edges, no outside or inside and cannot be properly construc

• Klein bottle, 1995

Callipers, used for artillery purposes, French, 17th century. Callipers were used to measure the diameter of cannon balls and the bores of cannons. This example also containd scales for artillery calculations

• Gunnery callipers, French, 17th century.

Napier's bones in brass, 17th century. John Napier (1550-1617), inventor of logarithms, also created this popular calculating tool known as Napier's cylindrical 'rods' or 'bones'. Napier's rods reduced muliplication to a sequence of simple additions

• Napier's bones, 17th century

Cordingley computometer adding machine c.1900. The Cordingley adding machine was one of several simple devices introduced around 1900. It is based on Blaise Pascal's (1623-1662) design of 250 years earlier.

• Cordingley's computometer', adding machine, c 1900.

'Tachypoly Plasiasme' ready reckoner, 1880-1884. Invented by C L Chambon in 1880, the 'Tachypoly plasiasme' ready reckoner showed multiplication tables up to 100 times 100.

• The 'Tachypoly Plasiasme' ready reckoner, 1880-1884

Harmonic analyser designed by O.Henrici, made by G. Coradi, 1894. Harmonic analysers were designed to break down a complex wave, such as a sound wave, into its fundamental and harmonic components. This one uses the motions of three glass spheres whic

• Henrici's harmonic analyser, No 3, 1894.

Model to show face-centre cubic packing made of ping-pong balls.1975. This model imitates a stuctural form found in crystals.

• Model depicting face-centred cubic packing, 1975.

6 figure engine counter by Schaeffer and Budenberg of Manchester, 1888. The counter could be used to count revolutions of a piece of mechanism or reciprocating actions.

• Mechanical counter, 1888.

Replica of a Bavarian counting cloth, 16th century. The original cloth is preserved at the Bavarian National Museum in Munich. Reckoning cloths were used as portable substitutes for counting boards. The letters on the cloth stand for various denomina

• Replica Bavarian reckoning cloth, German, 16th century.