Division by two

In mathematics, division by two or halving has also been called mediation or dimidiation.^[1] The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps.^[2] Some mathematicians as late as the sixteenth century continued to view halving as a separate operation,^[3]^[4] and it often continues to be treated separately in modern computer programming.^[5] Performing this operation is simple in decimal arithmetic, in the binary numeral system used in computer programming, and in other even-numbered bases. To divide an odd number by 2 use the mathematical solution ((N-1)÷2)+0.5. For example, if N=7, then ((7-1)÷2)+0.5=3.5, so 7÷2=3.5.

^ Steele, Robert (1922), The Earliest arithmetics in English, Early English Text Society, vol. 118, Oxford University Press, p. 82.
^ Chabert, Jean-Luc; Barbin, Évelyne (1999), A history of algorithms: from the pebble to the microchip, Springer-Verlag, p. 16, ISBN 978-3-540-63369-3.
^ Jackson, Lambert Lincoln (1906), The educational significance of sixteenth century arithmetic from the point of view of the present time, Contributions to education, vol. 8, Columbia University, p. 76.
^ Waters, E. G. R. (1929), "A Fifteenth Century French Algorism from Liége", Isis, 12 (2): 194–236, doi:10.1086/346408, JSTOR 224785, S2CID 144157808.
^ Wadleigh, Kevin R.; Crawford, Isom L. (2000), Software optimization for high-performance computing, Prentice Hall, p. 92, ISBN 978-0-13-017008-8.

[1] Steele, Robert (1922), The Earliest arithmetics in English, Early English Text Society, vol. 118, Oxford University Press, p. 82.

[2] Chabert, Jean-Luc; Barbin, Évelyne (1999), A history of algorithms: from the pebble to the microchip, Springer-Verlag, p. 16, ISBN 978-3-540-63369-3.

[3] Jackson, Lambert Lincoln (1906), The educational significance of sixteenth century arithmetic from the point of view of the present time, Contributions to education, vol. 8, Columbia University, p. 76.

[4] Waters, E. G. R. (1929), "A Fifteenth Century French Algorism from Liége", Isis, 12 (2): 194–236, doi:10.1086/346408, JSTOR 224785, S2CID 144157808.

[WC00-5] Wadleigh, Kevin R.; Crawford, Isom L. (2000), Software optimization for high-performance computing, Prentice Hall, p. 92, ISBN 978-0-13-017008-8.

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