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Topic: algebra doodle. (Read 1427 times) |
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Noke Lieu
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algebra doodle.
« on: May 10th, 2007, 11:52pm » |
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Thought I'd throw this up before I skip town (again)
came from an algebra doodle from a slow meeting. Nice, and Easy. Lovely.
How to square a 2 digit number:
Take a two digit number. (eg 25)
Round it up to teh nearest ten. (so 30)
Note the difference between the two. (so 5)
Subtract that from the original number (so 20)
Multipy the two numbers together (so 20 x30=600)
Square the difference, then add it. (so 5, 25, 625)
Ta da.
Why should this work?
Will try to pop in, but going to be more remote than I have been over the past few weeks.
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towr
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Re: algebra doodle.
« Reply #1 on: May 11th, 2007, 12:55am » |
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If we take 10a-b
then 10a*(10a-2b)+b2 = 100a2 -20ab+b2 = (10a-b)2
So in particular this is the case if 0 <= b < 10 and 0 < a <= 10
More general take a number a-b, then its square is
a*(a-2b)+b2 = a2 -2ab+b2 = (a-b)2
You can draw this out in a square to give a geometric argument
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Wikipedia, Google, Mathworld, Integer sequence DB
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Grimbal
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Re: algebra doodle.
« Reply #2 on: May 11th, 2007, 2:05am » |
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If the units digits is small, you can do it the other way round.
Example: 23
- round down: 20, difference 3.
- add the difference: 23+3 = 26
- multiply: 26*20 = 520
- add the difference squared: 520 + 32 = 529
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rmsgrey
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Re: algebra doodle.
« Reply #3 on: May 11th, 2007, 4:56am » |
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It follows trivially from:
(a+b)(a-b)=a2-b2
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ThudnBlunder
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Sameer
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Re: algebra doodle.
« Reply #5 on: May 14th, 2007, 12:08pm » |
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Reply after a long time... work keeping me busy.. but just to share one square method for numbers ending in 5 is pretty easy...
If you want to square 25 ...
Step 1. Square 5 -> 25
Step 2. Take first digit 2 and multiply it with next digit 3 = 6
Answer 625
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Proof is an idol before which the mathematician tortures himself.
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Grimbal
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Re: algebra doodle.
« Reply #6 on: May 14th, 2007, 1:29pm » |
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By the way, I participated in a maths contest. One problem involved computing squares of 2-digit numbers. We cannot use calculators. I was so happy to use the trick above.
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ThudnBlunder
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Re: algebra doodle.
« Reply #7 on: May 14th, 2007, 1:57pm » |
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on May 14th, 2007, 1:29pm, Grimbal wrote:| By the way, I participated in a maths contest. One problem involved computing squares of 2-digit numbers. |
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When was that? At school? (I trust you spotted my previously attached file of other neat ones.)
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Grimbal
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Re: algebra doodle.
« Reply #8 on: May 15th, 2007, 12:45am » |
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Last week-end.
It is the International Contest for Logical and Mathematical Games. It is actually a French contest, but other countries can participate as French regions. Most participants are French-speaking but you start to see other countries from East-Europe. It is mostly for school children and divided by school year, but there are two adult categories, easy and hard.
Yes, I saw your PDF. I haven't had the time to read all the tricks.
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