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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#226 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-26 09:14:14

IMPOSSIBLE!

15. is she more commonly known as the wife of someone famous?

#227 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-25 16:42:46

14. is she involved with medicine?

#228 Re: This is Cool » 0.9999....(recurring) = 1? » 2007-12-23 20:20:36

I was just thinking about this the other day. It really seems like the problem is not everyone here agrees that 0.999.... is equal to its limit. But also consider sqrt(2), its decimal representation can never be fully written out, just like 0.999..'s decimal value cannot be entirely written. any decimal number with a finite number of digits will always be less than or greater than sqrt(2), but still the actual value when squared, is 2. This being the case, so what if no amount of digits makes the decimal representation of 0.999 equal to 1? are you defining its value by what the decimal digits represent? or the decimal digits themselves?

#229 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-22 17:36:05

i'm going to give this a shot...

5. does the first letter of her first name come before n? (a to m)

that should help us later down the road

#230 Re: Dark Discussions at Cafe Infinity » My fears » 2007-12-21 08:29:29

worms! particularly, nightcrawlers. ew ew ew ew! i'm a guy but they still freak me out! especially when you try to pick them up and those small hair like extensions on their skin make them feel sticky, and they writhe and wriggle. That always makes me freak!

#231 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-20 17:28:39

I wonder if we could construct an elaborate tree of compound boolean expressions and ask the question giver "is this true?" and then modify it and ask again, systematically eliminating as many questions as possible in order to ask n questions in m turns with n < m.

#234 Re: Coder's Corner » super fast trig functions » 2007-12-15 12:06:49

hmmm... weird!

did you observe any jumps at some of the lower values as I did?

#235 Re: Puzzles and Games » Name this pattern » 2007-12-15 11:23:19

not unless you sing out w one syllable at a time like it was 3 separate letters, and then blaze through 'f e d' at the end. smile

#236 Re: Puzzles and Games » Name this pattern » 2007-12-15 09:51:32

the number of syllables in each letter of the alphabet? smile

#238 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-13 18:37:38

as usual we must ask

2. was he a scientist?

#239 Re: Coder's Corner » super fast trig functions » 2007-12-13 18:19:22

well i just tried testing it in java, however i had to start and stop the watch outside a for loop because the functions were too fast for the difference to turn out greater than zero. Anway, here's the code:

	
		int loops = 1000000;

		long startTime, stopTime, elapsedTime;


	for (int inputSize = 0; inputSize <= 3200000; inputSize += 100000)
		{
			startTime = System.currentTimeMillis();
			for (int i = 0; i < loops; i++)
			{

				Math.sin(inputSize);


			}
			stopTime = System.currentTimeMillis();

			elapsedTime = stopTime - startTime;

			System.out.println("input size: " + inputSize + " elapsed Time: " + elapsedTime );


		}


	}

output:

input size: 0 elapsed Time: 109
input size: 100000 elapsed Time: 437
input size: 200000 elapsed Time: 422
input size: 300000 elapsed Time: 422
input size: 400000 elapsed Time: 437
input size: 500000 elapsed Time: 438
input size: 600000 elapsed Time: 469
input size: 700000 elapsed Time: 421
input size: 800000 elapsed Time: 438
input size: 900000 elapsed Time: 437
input size: 1000000 elapsed Time: 454
input size: 1100000 elapsed Time: 406
input size: 1200000 elapsed Time: 437
input size: 1300000 elapsed Time: 422
input size: 1400000 elapsed Time: 438
input size: 1500000 elapsed Time: 422
input size: 1600000 elapsed Time: 421
input size: 1700000 elapsed Time: 2922
input size: 1800000 elapsed Time: 3016
input size: 1900000 elapsed Time: 2953
input size: 2000000 elapsed Time: 2843
input size: 2100000 elapsed Time: 2969
input size: 2200000 elapsed Time: 2625
input size: 2300000 elapsed Time: 2781
input size: 2400000 elapsed Time: 2719
input size: 2500000 elapsed Time: 2719
input size: 2600000 elapsed Time: 2906
input size: 2700000 elapsed Time: 2797
input size: 2800000 elapsed Time: 2797
input size: 2900000 elapsed Time: 2735
input size: 3000000 elapsed Time: 2750
input size: 3100000 elapsed Time: 2703
input size: 3200000 elapsed Time: 3047
Press any key to continue . . .

i tested it several times and it consistently jumped to a much longer time after about the 1.6 million mark. My guess is the algorithm checks to see if the input is bigger than something around 1.6 million and if so, does things differently.

#240 Re: Coder's Corner » super fast trig functions » 2007-12-13 13:05:27

well how do we measure the input size?  just in flat radians?

I'll try testing in both java and C++, and let you know what I find.

#241 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-13 12:58:16

good job, ganesh! have you had a turn yet?

#242 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-12 09:11:09

10. was she a political figure?

#243 Re: Euler Avenue » James Stirling Formula » 2007-12-12 07:55:02

Ricky wrote:

Bingo.

awesome! But are there any other restrictions that would do it?

#244 Re: Coder's Corner » super fast trig functions » 2007-12-12 07:48:11

sheesh! why are the library functions so fast? Do they use... magic?

#245 Re: Euler Avenue » James Stirling Formula » 2007-12-12 05:07:28

if the two limits each converge to the same finite number?

#246 Re: Coder's Corner » super fast trig functions » 2007-12-12 04:52:39

you're right! thats a wasted statement.

Perhaps now I should consider how many iterations are necessary based on the input size.

#248 Re: Help Me ! » Help with some calc » 2007-12-11 16:15:03

are you allowed to use l'Hopital's rule?

#249 Re: Dark Discussions at Cafe Infinity » Q20 » 2007-12-11 14:18:37

Hey, MathsIsFun hasn't had a turn yet! I vote he should go next.

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