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2. Napier's bones - Wikipedia

   en.wikipedia.org/wiki/Napier's_bones

   Napier gave details of a scheme for arranging the tables so that no rod has two copies of the same table, enabling every possible four-digit number to be represented by 4 of the 10 rods. A set of 20 rods, consisting of two identical copies of Napier's 10 rods, allows calculation with numbers of up to eight digits, and a set of 30 rods can be ...

3. Genaille–Lucas rulers - Wikipedia

   en.wikipedia.org/wiki/Genaille–Lucas_rulers

   A complete set of Genaille–Lucas rulers, including an additional index rod. Genaille–Lucas rulers (also known as Genaille's rods) are an arithmetic tool invented by Henri Genaille, a French railway engineer, in 1891. The device is a variant of Napier's bones. By representing the carry graphically, the user can read off the results of simple ...

4. Cuisenaire rods - Wikipedia

   en.wikipedia.org/wiki/Cuisenaire_rods

   Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on [1] way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. [2][3] In the early 1950s, Caleb Gattegno popularised this set of coloured number rods created ...

5. Multiplication table - Wikipedia

   en.wikipedia.org/wiki/Multiplication_table

   Multiplication table. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for ...

6. Rod calculus - Wikipedia

   en.wikipedia.org/wiki/Rod_calculus

   Start calculating from the highest place of the multiplicand (in the example, calculate 30×76, and then 8×76). Using the multiplication table 3 times 7 is 21. Place 21 in rods in the middle, with 1 aligned with the tens place of the multiplier (on top of 7). Then, 3 times 6 equals 18, place 18 as it is shown in the image.

7. Slonimski's Theorem - Wikipedia

   en.wikipedia.org/wiki/Slonimski's_Theorem

   Slonimski's Theorem is an observation by Hayyim Selig Slonimski that the sequence of carry digits in a multiplication table is the Farey sequence. This observation allowed Slonimski to create very compact multiplication tables for use in hand calculations. He received several awards for different devices for presenting these tables. The most ...