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#276 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2009-10-23 20:47:45
Try
[align=center]
[/align]for k = 1.4, 1.45 and 1.5. (In fact, try various values of k between 1.4 and 1.5 and see how it evolves.)
#277 Re: Exercises » Some nasty inequalities » 2009-10-22 11:27:33
I think you have the inequality sign the wrong way round.
#278 Re: Puzzles and Games » Find the area » 2009-10-20 22:45:51
Jane wrote:Some people clearly need to have their heads checked!
Comments like that hurt my feelings.
I wasnt referring to you; I was referring to The moronic Dude retard before you.
Fun fact: If two people have different opinions, it's not necessarily true that one of them is crazy.
Insults aside, it's a good discussion though. I suppose it depends what you mean by easier.
Lots of geometry problems like this one can be solved with calculus, so for some people, the first reaction on seeing this problem would be to set up an integral. In this case, it's easy to see how to do the problem, but doing the calculation might be trickier.
Other people, like Sophie, try to come up with a geometric way. The way she splits the 'complement region' into 4 congruent shapes is a beautiful idea, and I really like her method. However, she could only come up with that method after seeing this particular problem, and a similar question might not be solvable in the same way.
For people who can see geometric solutions like that easily though, I agree that getting to avoid the nasty integrals is a nice bonus.
Totally agree! 
#279 Re: Puzzles and Games » Find the area » 2009-10-20 16:46:53
I feel sorry for people who had to get through life before calculus.
#280 Re: Puzzles and Games » Find the area » 2009-10-20 03:00:33
If you didn't get
I got
As did Sophie: http://www.thescienceforum.com/viewtopi … 726#214726
#281 Re: Puzzles and Games » Find the area » 2009-10-20 02:34:52
TheDudes answer is what I got.
Now can you guys work out the problem without using integral calculus?
#282 Puzzles and Games » Find the area » 2009-10-19 20:37:35
- JaneFairfax
- Replies: 16
Four circles of radius 1 cm are drawn with their centres at the four verticies of a square with side length 1 cm. Find the area, in square centimetres, of the region overlapped by all four circles.
#283 Re: Exercises » Some nasty inequalities » 2009-10-16 23:00:51
#284 Re: Help Me ! » Derivatives » 2009-10-15 20:51:04
#285 Re: This is Cool » Mathematical terms in other languages » 2009-10-15 08:37:26
Maybe Binomial and/or Hypergeometric distributions or models?
That is correct.
#286 Re: Puzzles and Games » Janes number trap » 2009-10-11 10:26:19
Bobby is right, this is related to Happy Numbers.
A number is defined as Happy if it eventually goes to 1, and Unhappy if it eventually goes to the loop.
Yup.
#287 Re: Puzzles and Games » Janes number trap » 2009-10-11 10:25:15
I know Soroban has done one for cubes. If hes already done this for squares, then my apologies my search didnt turn up anything similar from Soroban.
Im not one hundred per cent about my proof yet if I do manage a proof, it probably wont be a rigorous one.
#288 Puzzles and Games » Janes number trap » 2009-10-11 09:44:13
- JaneFairfax
- Replies: 7
. .
. .
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#290 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2009-10-05 23:29:04
Try .
#291 Dark Discussions at Cafe Infinity » 1 in 14 million? » 2009-10-03 23:13:45
- JaneFairfax
- Replies: 3
http://news.bbc.co.uk/1/hi/world/europe/8259801.stm
The Bulgarian authorities have ordered an investigation after the same six numbers were drawn in two consecutive rounds of the national lottery.
The numbers 4, 15, 23, 24, 35 and 42 were chosen by a machine live on television on 6 and 10 September.
An official of the Bulgarian lottery said manipulation was impossible.
A mathematician said the chance of the same six numbers coming up twice in a row was one in four million. But he said coincidences did happen.
I think 1 in 4 million is wrong. It should be 1 in 14 million (i.e. 1 in ). There must be a misprint in the BBC article.
What do you guys think? 
#292 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2009-10-03 05:40:17
Try this.
y=abs(x)*tan(3*sqrt(x^2+y^2))Its actually an Archimedean spiral superimposed on its reflection in the y-axis (recall that an Archimedean spiral has the form r = aθ in polar coordinates). To fit more turns into the picture, try y=abs(x)*tan(4*sqrt(x^2+y^2)), y=abs(x)*tan(5*sqrt(x^2+y^2)), etc.
#293 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2009-10-03 01:01:45
Cool! Thats just what I need.
#294 Re: Help Me ! » How to construct a 10 degrees angle using compass and ruler » 2009-09-30 06:16:12
Aha. It appears that the answer given in yahoo answers allows you to measure the lengths of line segments. That is totally different then. I was thinking you were not allowed to use your ruler to measure lengths, only to draw straight lines in which case it would be provable, using an advanced mathematical branch called Galois theory, that it is impossible to construct a 10° angle.
And this is because the polynomial I stated above is irreducible in . If it were not irreducible, there would be an of the form with such that is a root of the polynomial above. I have just worked out that no such root of this form exists.
Obviously, if you are allowed to measure lengths with your ruler, you should be able to create more angles than if you were only using an unruled straightedge. Happy constructing. 
#295 Re: Help Me ! » How to construct a 10 degrees angle using compass and ruler » 2009-09-30 02:43:54
http://en.wikipedia.org/wiki/Angle_trisection
Constructing a 10° angle would mean trisecting the angle 30°. So, is the polynomial
[align=center]
[/align]irreducible over the field
? If yes, then you cannot trisect 30° and hence construct a 10°; if not, then you can do it.#296 Re: Jokes » "Have I Got News For You" » 2009-09-29 10:11:53
At last!!
Thanks for explaining everything. I would have appreciated it so much more if you had explained your action straightaway.
Now, as you are the owner of this site, you have the right to allow and disallow anything you want on the site. I have no objection to that. BUT I DO NOT TAKE KINDLY TO BEING TREATED WITH RUDENESS, OKAY?
#297 Maths Is Fun - Suggestions and Comments » Deletion of posts v deletion of threads » 2009-09-29 08:34:45
- JaneFairfax
- Replies: 0
MathsIsFun, I understand that you are busy and I'm very grateful for what you do in maintaining these forums, but do you think that next time if the first post in a thread is offensive you could just edit the post (wipe it clean) instead of deleting it?
#298 Re: Jokes » American » 2009-09-29 00:13:36
Thanks, Identity.
I have sent an email to MathsIsFun demanding an explanation for that outrageous action.
#299 Re: Jokes » American » 2009-09-28 23:47:03
And these were the replies in the original thread.
Hi Jane;
Personally, I can't see why it is called either. Sometimes you go down, an action not described by either name.
We are not tiresome, we just seem that way.
I've always called it a lift. Except for when I was in America... Wow, that's strange. But in this case I agree with bobby.
Hi all;
You can never go wrong agreeing with bobbym.
An Englishman walks into a bar. "Oh my goodness, how silly of me. Wonder why I didn't see that bar there? Perfectly obvious bar. Oh well ... never mind ..." (passes out)
I've always called it a lift. Except for when I was in America... Wow, that's strange. But in this case I agree with bobby.
#300 Jokes » American » 2009-09-28 23:42:13
- JaneFairfax
- Replies: 4
I started a thread on this some time ago, but the thread was deleted presumably because of one or two offensive posts in it. I will start the same thread again.
[snip]