1. Counting

# 1. Counting - Hieroglyphics Place-value system O Babylonian...

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What’s in a number? A brief history of numbers and counting (material from Pi in the Sky , John Barrow)

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Uses of numbers O counting O calculating O representing the world O performing logic O knowing truth O doing mathematics
Why bother to count?

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How many objects?
Finger counting O Allows large numbers O Greek/Roman origin O Add gestures for more numbers O 10 fingers -> base 10 counting

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2-counters
10- & 20-counters

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Decimal system O All currently known counting systems based on 2, 5, 10, 20 & 60 O 10 is convenient O Base-12 has merits (two-left), and remnants
“sacred picture writing”, < 3000 BC, for permanent records (a,b) • hieratic (c) and demotic (d) scripts for everyday work • (d) requires the fewest pen marks

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Unformatted text preview: Hieroglyphics Place-value system O Babylonian, 2000 BC O note base-60 O two wedge shapes in clay tablets O no symbol for 0 O e.g. meaning of << is ambiguous The invention of zero O Babylonian, 300-200 BC O Mayan, Chinese & Indian cultures, independently O Meaning of 0: null, space, 10-10 Indian numerals • 2500 BC, system is complete 1. unique symbols 1-9 2. base-10 3. place-value notation 4. has zero “the most successful intellectual innovation ever made on our planet” Algorists vs Abacists • Algorist smugly demonstrates memory, place-value, fractions. • Dame Arithmetica presides in judgement -- with Indo-Arabic numerals on her gown!...
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1. Counting - Hieroglyphics Place-value system O Babylonian...

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