10-16-2002, 07:19 PM | #21 | |
Symbol of Cyric
Join Date: March 29, 2001
Location: Twititania, Europe
Age: 63
Posts: 1,221
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Quote:
You'll be lecturing us(s) on maths next - what is the square root of 3 by the way? You are such a doughnut sometimes Lanesra! Please write out 100 times 'Pot, Kettle, Black'[/QUOTE]Hope this helps you out o clever one , it took me ages to type , I'm suprised you didn't know , after all you're the one with the oligy. The Irrationality of Problem: Prove that is an irrational number. Solution: The number, , is irrational, ie., it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us assume that is rational so that we may write = a/b 1. for a and b = any two integers. We must then show that no two such integers can be found. We begin by squaring both sides of eq. 1: 3 = a2/b2 2. or 3b2 = a2 2a. If b is odd, then b2 is odd; in this case, a2 and a are also odd. Similarly, if b is even, then b2, a2, and a are even. Since any choice of even values of a and b leads to a ratio a/b that can be reduced by canceling a common factor of 2, we must assume that a and b are odd, and that the ratio a/b is already reduced to smallest possible terms. With a and b both odd, we may write a = 2m + 1 3. and b = 2n +1 4. where we require m and n to be integers (to ensure integer values of a and b). When these expressions are substituted into eq. 2a, we obtain 3(4n2 + 4n + 1) = 4m2 + 4m + 1 5. Upon performing some algebra, we acquire the further expression 6n2 + 6n + 1 = 2(m2 + m) 6. The Left Hand Side of eq. 3a is an odd integer. The Right Hand Side, on the other hand, is an even integer. There are no solutions for eq. 3a. Therefore, integer values of a and b which satisfy the relationship = a/b cannot be found. We are forced to conclude that is irrational. [ 10-16-2002, 07:20 PM: Message edited by: Lanesra ] |
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10-17-2002, 12:46 AM | #22 | |
Thoth - Egyptian God of Wisdom
Join Date: May 10, 2002
Location: Dunedin, New Zealand.
Age: 42
Posts: 2,860
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[quote]Originally posted by Melusine:
[QB] Quote:
Strewth! Crikey!
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[img]\"hosted/Hierophant.jpg\" alt=\" - \" /><br />Strewth! |
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10-17-2002, 01:49 AM | #23 | |
20th Level Warrior
Join Date: November 16, 2001
Location: Estonia
Age: 35
Posts: 2,775
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Quote:
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10-17-2002, 03:41 AM | #24 |
Manshoon
Join Date: March 27, 2002
Location: Brisbane, Australia
Age: 38
Posts: 248
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i think all of my teachers have been pretty good except for a few....
in year 2 our teacher made spelling mistakes on posters in our classroom which some of the parents of children in my class had to correct for her.... also have a physics teacher now who does not understand some things he teaches us, just tells us to read the text book.... [ 10-17-2002, 03:42 AM: Message edited by: lethoso ]
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the three r\'s of microsoft product support: reboot, retry, reinstall |
10-17-2002, 05:11 AM | #25 |
Symbol of Cyric
Join Date: July 11, 2002
Location: NZ
Age: 37
Posts: 1,268
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Don't get me started about my english teacher. She is supposed to have qualifications in Speech/Drama, but cannot pronounce words such as 'says' and 'research'.
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If possible, I want to relive my life... not as a devil. This time, someone like you. |
10-17-2002, 12:35 PM | #26 | |
Zartan
Join Date: March 1, 2001
Location: London, England
Age: 53
Posts: 5,164
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Quote:
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10-17-2002, 12:39 PM | #27 |
Jack Burton
Join Date: May 2, 2002
Location: Canterbury, England
Age: 36
Posts: 5,817
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Luckily, uss, I'm going to be an english teacher. try not to cry too loudly
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10-19-2002, 03:54 AM | #28 | |
Jack Burton
Join Date: March 1, 2001
Location: Airstrip One
Age: 40
Posts: 5,571
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Quote:
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[img]\"http://www.wheatsheaf.freeserve.co.uk/roastspurs.gif\" alt=\" - \" /> <br />Proud member of the Axis of Upheaval<br />Official Titterer of the Laughing Hyenas<br />Josiah Bartlet - the best President the US never had.<br />The 1st D in the D & D Show |
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