Manfred Börgens
Mathematics on stamps
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deutsche Flagge  deutsche Version
left: portrait Adam Riese, right: addition scheme   Germany 1959 and 1992

  Scott 799 and 1748

Arithmetic teacher Adam Riese (1492 - 1559)

Adam Riese (his correct name was "Ries") is well known in Germany as a master of arithmetic. To his contemporaries, he was famous as "Hofarithmeticus" (court arithmeticus) at the Saxonian court and for his arithmetic books which quickly spread throughout Germany due to letterpress printing that had been recently invented. Adam Riese never attended university but could teach merchants paper and pencil division, a task that was considered too difficult for students of most universities of that time.

Both stamps (commemorating the 4th centenary of Riese's death and the 5th centenary of his birth, respectively) show the Adam Riese "trade mark", a cross with four numbers. The stamps show pairs of equal numbers, but this does not represent the general case. Thus the rule behind these number crosses cannot easily be guessed.

Riese's number cross is a scheme for checking an addition. This check is known as "casting out nines". An addition  a + b = c  is checked by computing:

A = a mod 9

B = b mod 9

C = c mod 9

D = A + B

A, B, C, D are put into Riese's cross:

top D, bottom C, left A, right B

The check is successful if  C = D  or  C + 9 = D .

First example:


top 3, bottom 3, left 1, right 2

Second example:


top 13, bottom 4, left 7, right 6

last update  2005-01-30
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