When the Kaktovik middle school students who invented the system graduated to the high school in Barrow, Alaska (now renamed Utqiaġvik), in 1995, they took their invention with them. They have been introduced into language-immersion programs and have helped revive base-20 counting, which had been falling into disuse among the Iñupiat due to the prevalence of the base-10 system in English-medium schools. The Kaktovik numerals have gained wide use among Alaskan Iñupiat. In the above example the factor (6) is not found in the table, but its components, x24px|□ (1) and (5), are. These tables are functionally complete for multiplication operations using Kaktovik numerals, but for factors with both bases and sub-bases it is necessary to first disassociate them: Ī simplified multiplication table can be made by first finding the products of each base digit, then the products of the bases and the sub-bases, and finally the product of each sub-base: The students could keep track of the strokes of the intermediate steps with colored pencils in an elaborated system of chunking. The visual aspects and the sub-base of five made long division with large dividends almost as easy as short division, as it didn't require writing in subtables for multiplying and subtracting the intermediate steps. For example,Īnother advantage came in doing long division. It was even easier for subtraction: one could simply look at the number and remove the appropriate number of strokes to get the answer. Adding two digits together would look like their sum. □ goes into the first three digits of the dividend twice (traced in red and blue), for a two in the quotient (red and blue), into the next three once (green), does not fit into the next (zero in the quotient), and into the remaining white digits once.Īn advantage the students discovered of their new system was that arithmetic was easier than with the Arabic numerals. This proved visually helpful in doing arithmetic. ![]() In this way, they created a iconic notation with the sub-base of 5 forming the upper part of the digit, and the remainder forming the lower part. When the middle-school pupils began to teach their new system to younger students in the school, the younger students tended to squeeze the numbers down to fit inside the same-sized block. The Iñupiaq language does not have a word for zero, and the students decided that the Kaktovik digit 0 should look like crossed arms, meaning that nothing was being counted. In base-20 positional notation, the number twenty is written with the digit for 1 followed by the digit for 0. Aesthetics: They should be pleasing to look at. ![]()
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