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------------------------------ 1966 - Math - the easy way.
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- This teacher had an unruly class. So she tried to occupy them with this simple problem. Add up all the whole numbers from 1 to 100.
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- Carl Fredrich Gauss quickly blurted out the answer 5,050.
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- “Carl, how did you do the math so fast?” In your head?
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- Well, recognize that 1 to 100 is a series. Take the first 1 and add it to the last 100 and you get 101. Add 2 to 99 and you get 101. Add 3 to 98 and you get 101, …………. 50 + 51 = 101. Do that 50 times and you get 5,050.
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- You can do the same trick adding up all the numbers from 1 to 1,000.
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- 500 pairs of 1,001 and you get 500,500.
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- How about adding all the even numbers from 2 to 2,000.
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- OK, that is tougher. We need a short cut . We already did half that adding up 1 to 1,000. So, 2 * 500,500 = 1,001,000.
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- Add all the odd numbers from 1 to 1,001. That is tougher still. The trick is to recognize the formula for the series:
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- Here is the series: 1 + 3 + 5 + 7 + …………. + (2n -1)
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--------------------------1, 2, 3, 4, , ……….. = “n”
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------------ SUMS = 1 , 4, 9, 16, ………… = n^2
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------------- sum of the series (2n - 1) = n^2
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------------- sum of the series = n@ = 500^2 = 250,000
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- Carl had many different ideas using math. The teacher was teaching how to add up columns of numbers from left to right then carry to the left when necessary.
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--------------------------- 127
--------------------------- 301
------------------------ + 546
-------------------------------------
--------------------------- 974
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- Carl , said watch this teacher, this is easier adding right to left: And you can do it in your head:
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---------------------------- 100 ------- 20 ----- 7
---------------------------- 300 ------- 0 ----- 1
------------------------- + 500 ------ 40 ----- 6
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--------------------------- 900 ------- 60 ----- 14 = 974
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- Another problem:
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----------------------------- 241
----------------------------- 130
-------------------------- + 427
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---------------------------- 798
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- Carl , said watch this teacher, this is easier adding right to left:
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---------------------------- 200 ------- 40 ----- 1
---------------------------- 100 ------ 30 ----- 0
------------------------- + 400 ------ 20 ----- 7
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--------------------------- 700 ------- 90 ----- 8 = 798
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- There are a lot of these tricks. To divide a number by 5, first multiply by 10 then divide by 2.
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- Say you at McDonald’s and you hamburgers and shakes come to $26.14. And, she is cute, you want to add a 15% tip.
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----------------------- 10% = $2.61
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------------------------ 5% = $1.30
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---------------------- 15% = $3.91
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- Give the girl a $4 tip and be done with it.
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- You can remember “ pi” to 6 digits by:
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----------- “ May I draw a round perimeter?”
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-------------” 3. 1 4 1 5 9
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- Pi = 3.14159.…………
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- Get it?
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- The study of math cultivates the reasoning. It is the best discipline for the mind and the best mental training for the world you are entering. Always do the math.
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- Note (1): Request any of the Reviews by number to learn more. There are dozens more.
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----- 707-536-3272 ---------------- Wednesday, April 5, 2017 -----
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