Shortcomings of the Egyptian System

Transcript

Shortcomings of the Egyptian SystemIn the Egyptian system, every time you reach a new power of 10 (1, 10, 100, 1000...), you need a completely new symbol. 1 = Stroke 10 = Arch 100 = Spiral ...and so on. The Shortcoming: If you wanted to write a number ten times bigger than the largest symbol you had, you couldn't just add a zero or move a digit over. You had to invent a brand new drawing. If numbers kept getting bigger forever, you would need an infinite number of different drawings! The Question: Can there be a number whose representation in Egyptian numerals has one of the symbols occurring 10 or more times? Why not? The Answer: No, it is impossible for a valid Egyptian numeral to have 10 identical symbols. Reason: The Egyptian system is a Base-10 grouping system. This means it follows a strict rule of "Regrouping" or "Trading Up": As soon as you collect 10 Strokes (|), you must trade them for 1 Arch (⋂) As soon as you collect 10 Arches (⋂), you must trade them for 1 Spiral Because of this rule, the maximum number of identical symbols you can ever write in a row is 9. If you wrote the 10th one, the group would instantly transform into the next larger symbol1.