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Napier’s Rods

Napier’s Rods. Napier WHO????. John Napier: Born 1550- Died 1617 Lived in Edinburgh Scotland during time of Protestantism Came from a wealthy family/background. Man of many talents, decent values and high intelligence (attended University of St. Andrews at the age of 13).

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Napier’s Rods

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  1. Napier’s Rods

  2. Napier WHO????... • John Napier: Born 1550- Died 1617 • Lived in Edinburgh Scotland during time of Protestantism • Came from a wealthy family/background. • Man of many talents, decent values and high intelligence (attended University of St. Andrews at the age of 13). • Spent his time studying mathematics, and developing new tools and formulas to make the process of calculation easier. • Napier's free time led to invention of  Napier’s Rods, type of counting system • However most famous for his publication of a book of Logs

  3. Napier’s WHAT????..... • Napier’s Rod’s, a.k.a. Napier’s Bones, is a type of abacus (counting frame) that simplified finding multiplication equations • In addition, rods could be used to find division and square roots

  4. Okay… So How do I Use It???.... • To use Napier's rods ,you need ten strips of paper each divided into 9 parts, one for each of the first 9 multiples of the number at the top of strip as shown below

  5. Multiplication!!!!!!!! • We can use Napier’s Rods to multiply any two numbers • Lets start simple… • E.g Take the equation 75 x 3 • Place the multiplier, the '7' and the '5' bone side by side (for 75) as shown to the right. • To calculate, sum the numbers along the slanted diagonals of the combined bones using the row applying to the multiplier •  For the two bones, when reading from right to left there are three diagonals which represent units, tens and hundreds when the multiplier is three •  5 represents 5 units, the 1+1=2 represents 2 tens, and the 2 represents 2 hundreds. • Adding 5 units, 2 tens and 2 hundreds gives 225. 75 X 3 = 225

  6. That Was Pretty Easy… • Napier intended for his homemade calculator to solve BIGGER multiplication problems… • E.g. Take the equation 84 x 24 • place the multiplier and the bones '8' and '3' bones, for 83, side by side as shown to the right • To find the product first multiply by 4 and then multiply by 20 • add just as you would for long multiplication to find the answer. • Final answer: 1992

  7. Lets Go Crazy!!!!!!!! • Okay lets get a little more complicated: 7 x 46785399 • Once again, to solve multiply number by 7 then combined diagonal bones through addition • Final answer: 327,497,793

  8. Alright this is ridiculous… • Last example: 46785399 x 96431 • Top number should be the bigger number multiplied by the smaller number on the side. Add entire sum • Make sure to distinguish unit, tens, hundreds, etc. digits. • Final answer: 4,511,562,810,969

  9. Okay Your Turn!!!!!!!!!!!

  10. The End

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