Mathematics

Single surface models made by Alan Bennett in Bedford, 1995. Three toroid single surface vessels, one with the loop inside the torus, one with a narrow loop outside and one with a wider loop outside. All can be cut to produce a pair of single-twist M

• Klein bottles, 1995

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.

Six inch silver sector signed "Ramsden, London" with attached set square, late 18th century. Sectors were used from the end of the 16th century until the mid 19th century for calculations involving proportion. They were ingraved with logarithmic and

• Six inch silver sector, late 18th century.

Replica of a quipu made from an original held at the Museum of Natural History, New York, in 1974. Quipus were used by the Incas during the 15th and early 16th centuries as records of all types of accounts. It was discovered in the early 20th century

• Replica quipu, South American, c 15th century.

Wine diagonal, a type of gauging rod, by J.Stutchbury, 1797-1826. These were used by Excise Officers together with slide rules to calculate the volume of wine in wine casks, and thence the duty payable. Until 1826 the volume of a wine gallon was diff

• Wine diagonal, 1797-1826.

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.

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.