Answered: Find the reciprocals, using a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the reciprocals, using a Mesopotamian method. (You can use modern numeration, but MUST use one of the Mesopotamian methods of finding a reciprocal): Reciprocal of 12. Reciprocal of 20. Reciprocal of 75.

Expert Solution

Step 1: Reciprocal of 12:

Finding reciprocals using the Mesopotamian method involves using the ancient Babylonian method, which was based on the sexagesimal (base-60) numeral system. Here's how you can find the reciprocals of 12, 20, and 75 using this method:

Reciprocal of 12:

Step 1: Start with a guess for the reciprocal, let's say 5, which is a common choice.

Step 2: Multiply the guess (5) by the number (12) to get 60.

Step 3: Subtract the result (60) from 360 (which is 60 times 6, representing the sexagesimal base) to get 300.

Step 4: Divide 300 by the original number (12) to get the reciprocal.

$R e c i p r o c a l space o f space 12 space almost equal to space 300 over 12 space equals space 25$

So, the reciprocal of 12 is approximately 25 in the Mesopotamian system.