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#26 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-05 01:04:21
Problem # k + 23
A Pythagorean triple is a set of three numbers (a,b,c) such that
a² + b² = c². For example, (3,4,5).
Prove that three prime numbers cannot form a Pthagorean triple.
Case 1:
Prime numbers are all odd except 2, so a² is odd, b² is odd, and c² is also odd. But, a²+b² is even if both of them are odd. Contradiction!!
Case 2:
a=2
4+b²=c²
c²-b²=4
(c-b)(c+b)=4
the only possibilities are (c-b)=1, (c+b)=4
2c=5
c=2.5 (rejected)
Case 3:
a=b=2
4+4=c²
c²=8^0.5 (rejected)
Case 4:
a=b=c=2 (rejected immediately :P)
#27 Re: Jokes » Limericks » 2005-10-05 00:56:10
There was once a man with Asperger's
Who liked to eat sweet oranges.
One day, he choked,
While drinking a Coke,
And watching an unknown stranger.
#28 Re: This is Cool » 0 = 1 » 2005-10-05 00:50:39
it is essential that 0!=1 in combinatorics, otherwise a lot of things won't work
#29 Re: Help Me ! » square root accuracy » 2005-10-05 00:47:53
cosine and sine can be calculated using maclaurin's expansion
#30 Dark Discussions at Cafe Infinity » Asperger's Syndrome » 2005-10-05 00:43:32
- wcy
- Replies: 6
I just read up a bit on Asperger's Syndrome, and one of the symptoms is a persistent interest in certain topics like say, mathematics!!
Visit my website http://www.geocities.com/asperger_sg and try out the diagnostic tests and see if you have AS!
#31 Re: Help Me ! » Homework problems » 2005-09-13 21:31:53
x/(x-1) +3 = 1/(x-1)
subtract 1/(x-1) on both sides
(x-1)/(x-1) +3=0
1+3=0
contradiction
therefore no solution
#32 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-31 19:39:11
my answer is
#33 Re: This is Cool » 2n ones and n twos » 2005-08-31 19:35:46
wow this is amazing
#34 Re: Help Me ! » Converting 3.14159265358979323846 into base-26 using alphabet » 2005-08-31 19:33:14
visit http://www.geocities.com/chengyuanwu/baseconverter.html for a base converter.
removing the decimal point, i get A4AJ8AI
#35 Re: Jokes » Mathematics jokes » 2005-08-27 23:13:25
lol!!! really funny
#36 Re: Dark Discussions at Cafe Infinity » Venting. Do not read if you; are under 13 or; have a heart condition. » 2005-08-27 23:11:17
yeah life isnt all about grades
there is always more to life than you know
#37 Re: Introductions » To introduce myself. » 2005-08-27 23:08:42
javascript rox!!
#38 Re: Help Me ! » IMPT: Probability Question » 2005-08-27 23:06:41
1) 35/350=0.1
2)Chance that nobody gets a prize -- 0.9^10=0.34867844
Chance that at least one person gets a prize-- 1-0.34867844=0.65132156
3) 0.1^10=1.0 × 10-10 (which is very low)
#39 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-27 22:10:23
what happened to the old problems before the forum got hacked?
#40 Re: This is Cool » Strange formula » 2005-08-27 22:09:19
i think it can be proven by dividing the polygon into many smaller polygons, eg triangles
#41 Re: Help Me ! » Variations » 2005-08-27 22:07:12
if y is inversely proportional to x then y=k/x, where k is a constant
#42 Re: Maths Is Fun - Suggestions and Comments » Online poll for website » 2005-08-23 23:00:14
my bathroom is full of weird, semi-transparent spiders, which are really really thin
#43 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-23 22:56:28
this could be done by drawing a Venn diagram, i suppose
#44 Re: Dark Discussions at Cafe Infinity » Music; what's your song? » 2005-08-23 22:54:29
anyone listens to classical music?
#45 Re: Puzzles and Games » Two emailed Puzzles » 2005-08-23 22:53:23
Another way:
33-3+3/3=33-3+1=31
#46 Re: Jokes » funny one » 2005-08-23 22:48:32
why is first of April so tired?
it comes after 31 days of March
#47 Re: Dark Discussions at Cafe Infinity » Wink Murder 3 » 2005-08-23 22:46:33
i would like to play too, but i don't know the rules of the game
#48 Re: Guestbook » if there is any hackers out there get lost and read this » 2005-08-23 22:45:13
i really don't see why hackers would want to deface this forum...
those hackers really have no moral conscience at all...
this is an academic website, not a political website nor does it have any controversial views or anything like that...
#49 Re: Introductions » Mikau's Introduction » 2005-08-23 22:43:33
don't worry, it is never too late to learn maths
#50 Re: This is Cool » A Pi Fundraiser » 2005-08-23 22:42:32
hope you get your share of the pi(e) !! 