Archimedes, the Divisible Apple

From the early 1800s, teachers advocated the use of devices to teach arithmetic, proposing objects such as the blackboard and the teaching abacus. To illustrate the meaning of fractions, some brought an apple to class and cut it up. By the 1920s, some made special beads for the teaching abacus, divided to represent fractions. Hugo Jung of Stuttgart, Germany, developed an improved version of this apparatus. His “apples” were to have a hollow metal core, attached to a flange that allowed various fractions to be removed (halves, thirds, etc.). The core would then slide on the rods of a numeral frame. In this form of his apples, the core is solid, and individual apples are used to teach students about specific fractions.
The set consists of nine varnished wooden balls, sliced into segments representing fractions. A metal flange at the base of each apple holds both a central cylindrical core that runs through it and metal pins that hold the various slices in place. The first of the nine “apples” is divided into two halves, the second into three thirds, and the third into one half and two fourths. The fourth apple is divided into five fifths, the fifth into one half and three sixths, and the sixth into seven sevenths. The seventh is divided into one half, one fourth, and two eighths. The eighth apple has two thirds and three ninths and the last has one half, two fifths, and one tenth.
The balls fit into a square cardboard box that is divided into nine compartments. A label glued to the inside of the box reads: “ARCHIMEDES” (/) the divisible apple to learn the calculation of fractions.; Made in Germany; Protected by patent in all civilised countries [/] D.R.P. No. 489 439; Sole manufacturer: Rudolf Loebelenz, Stuttgart.
Hugo Jung, D.R.P. 489,439, July 23, 1930.
Hugo Jung, British Patent 343,323, February 24, 1930.
Hugo Jung, Swiss Patent 145,722, May 16, 1931.
Currently not on view
Object Name
geometric models, set of
date made
ca 1930
Loebelenz, Rudolf
Physical Description
wood (overall material)
metal (overall material)
cardboard (overall material)
overall: 6.3 cm x 21.4 cm x 21.4 cm; 2 1/2 in x 8 7/16 in x 8 7/16 in
place made
Deutschland: Baden-Württemberg, Stuttgart
ID Number
catalog number
accession number
Learning Arithmetic
Science & Mathematics
Arithmetic Teaching
See more items in
Medicine and Science: Mathematics
Learning Arithmetic
Arithmetic Teaching
Data Source
National Museum of American History, Kenneth E. Behring Center
Additional Media

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