Search found 2071 matches

by jaap
Thu Jul 30, 2015 12:50 pm UTC
Forum: Mathematics
Topic: New type of pentagonal tile
Replies: 6
Views: 30816

New type of pentagonal tile

A new type of tileable pentagon has been found! There are many kinds of tiling that use just one shape of pentagonal tile (and its mirror image if necessary). Up to now, these tiles fell into 14 types (see http://www.mathpuzzle.com/tilepent.html ). Now another has been found. type15.png I did a lot ...
by jaap
Fri Jul 24, 2015 2:45 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 120944

Re: Math: Fleeting Thoughts

I've been reading graph theory -- the definition of adjacency keeps giving me trouble. Everything I read describes adjacency as one of two things: Vertices connected by an edge, or vertices that share an edge. However, both 'connected' and 'shared' confuse me when it comes to directed edges: If X a...
by jaap
Sat Jul 18, 2015 9:53 pm UTC
Forum: Mathematics
Topic: sum and product of natural number
Replies: 9
Views: 2744

Re: sum and product of natural number

snip If B says yes to the first question, doesn't that mean it could be any number with only two divisors? If B says no then that excludes a=b=1; all a=p, b=1; a=p1, b=p2. Where p, p1, p2 are prime and p1=!p2 The number p1*p2 has four divisors, namely 1, p1, p2, and p1*p2 - there are two ways t...
by jaap
Fri Jul 17, 2015 8:38 am UTC
Forum: Mathematics
Topic: Pairwise Differences
Replies: 3
Views: 1464

Re: Pairwise Differences

The set of numbers evenly divisible by n is closed under talking the set of pairwise differences. Are there any sets of natural numbers with this property that are not subsets of any set in the above class? In particular, I'm interested in those that, like the above, can be truncated to n elements ...
by jaap
Thu Jul 16, 2015 5:05 am UTC
Forum: Language/Linguistics
Topic: Words You Didn't Know That Describe Things Perfectly
Replies: 91
Views: 25503

Re: Words You Didn't Know That Describe Things Perfectly

Cornobble (archaic): to hit with a fish. Can anyone provide any reference for this being a real thing? The OED online says it isn't, and I can't find any reputable source. I heard it mentioned on the "Says You" podcast, and the host claims to have read it in a book, but I am dubious. I ha...
by jaap
Wed Jul 15, 2015 12:03 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9862
Views: 1762406

Re: Coding: Fleeting Thoughts

I really hate that C++ calls its dynamic array a "vector" - then when I want to use my own type, I have to call it a column_matrix to avoid confusion, even though my type - an immutable, fixed-length, passed by value array that supports scalar addition and xor, scalar multiplication, and ...
by jaap
Tue Jul 14, 2015 10:51 am UTC
Forum: Science
Topic: Conductors and Motors/Generators
Replies: 7
Views: 1763

Re: Conductors and Motors/Generators

Rambling on, it occurred to me that a liquid would be awkward in terms of the brushes, so why not make the winding rigid and allow the magnets to rotate. Then I wondered why all the motors I've seen always rotate the winding - wouldn't it be easier in general to rotate the magnets and avoid the nee...
by jaap
Thu Jul 09, 2015 4:15 pm UTC
Forum: Mathematics
Topic: Marks and Integers
Replies: 3
Views: 1500

Re: Marks and Integers

by jaap
Wed Jul 08, 2015 7:20 am UTC
Forum: Mathematics
Topic: Wanted: Elegant proof of sin(x)/x limit
Replies: 49
Views: 8028

Re: Wanted: Elegant proof of sin(x)/x limit

Qaanol wrote:
jestingrabbit wrote:I claim |BD| < |BE|+|ED|
<snip>
verified by good sense

That’s the part I’m struggling to prove cleanly.

This is the Triangle Inequality and that wiki page has a short euclidean proof.
by jaap
Sun Jul 05, 2015 3:27 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 4236

Re: Factorial expressed as sum of consecutive numbers

Thank you for your comments and computations. Now we assume that the maximal length of the consecutive positive numbers is solved. So we could express n!=S(f,l) where f is the first number of the sequence and l the last number of the sequence. S(f,l) is the summation. The next step is computing S(f...
by jaap
Fri Jul 03, 2015 9:40 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 4236

Re: Factorial expressed as sum of consecutive numbers

Can we conjecture that as n grows the length is ALWAYS an odd number? A factorial can be expressed as equal to A*B where A = 2^k and B an odd number. Limit of the ratio A/B = 0 as n grows to infinity. Does it imply that the length will be always odd? No. You asked for the longest such sequence, whi...
by jaap
Fri Jul 03, 2015 1:05 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 4236

Re: Factorial expressed as sum of consecutive numbers

There is still one hurdle to get over : the complexity. As n grows can we apply this algorithm with minimal complexity. What will be the complexity if n is 500 digits number? I`m not programmer so I just want to know if we can do it in reasonable time. If n is 500 digits, i.e. is about 10^500, then...
by jaap
Fri Jul 03, 2015 12:18 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 4236

Re: Factorial expressed as sum of consecutive numbers

Here's a way to do it. Take 2*n!, and write it as a product a*b, with: - a and b of differing parities (i.e. one is odd and one is even but it does not matter which is which) - a and b as close to each other as possible, (i.e. as near to sqrt(2*n!) as possible) - a<b Then n! is equal to the sum of a...
by jaap
Thu Jun 18, 2015 5:53 am UTC
Forum: Coding
Topic: Happy bases
Replies: 12
Views: 3323

Re: Happy bases

Find a more efficient algorithm to determine whether a number is happy in a given base. One thing I've noticed is that you immediately forget all previous calculations. If you've verified all numbers from 1 to n-1 to be happy, you only need to calculate the sequence for n until reaching any number ...
by jaap
Tue Jun 09, 2015 12:16 pm UTC
Forum: Mathematics
Topic: Independent repeated trials and mutually exclusive events.
Replies: 4
Views: 1854

Re: Independent repeated trials and mutually exclusive event

Mutually exclusive is just a fancy term for saying that there is no overlap between the events. For instance, if I wanted to know the number of people in my class who are either women or math majors, I can't add the number of women to the number of math majors because that would double-count all th...
by jaap
Sat Jun 06, 2015 4:24 pm UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 150207

Re: Project Euler

@jaap: Would you mind referring me to a simple memoized implementation of a factorial method in Java? That would probably help me a lot, just seeing how the memoization is implemented.... Actually, maybe I do know enough to implement it. I suppose you would have to have it in its own class so a fie...
by jaap
Wed Jun 03, 2015 2:53 pm UTC
Forum: Coding
Topic: Reflection around the inside of a circle
Replies: 4
Views: 3074

Re: Reflection around the inside of a circle

I always found it easier to do this kind of thing with vectors, I always make mistakes with trigonometric calculations. And calculating a normal vector for a sphere is really easy. I totally agree. In most languages I've seen, atan2 has the y parameter first, so reflectTangent isn't actually the ta...
by jaap
Tue Jun 02, 2015 10:41 pm UTC
Forum: Mathematics
Topic: Combinations algorithm and property
Replies: 19
Views: 3054

Re: Combinations algorithm and property

The loop part (that the last one is the neighbour of the first one) makes this tricky. Without that part I would solve it by methodically moving freespaces (assuming I didn't misunderstand something). That does indeed work as far as I can tell for a non-circular list. Here is some Java code that do...
by jaap
Tue Jun 02, 2015 3:19 pm UTC
Forum: Mathematics
Topic: Combinations algorithm and property
Replies: 19
Views: 3054

Re: Combinations algorithm and property

In other words - A set with n elements has nCk subsets of k elements. Find a way to put these subsets in a (circular) list such that each adjacent pair of subsets in the list have k-1 elements in common. Preferably find an algorithm that allows you to generate such a list. This feels a bit like a Gr...
by jaap
Tue Jun 02, 2015 11:52 am UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 150207

Re: Project Euler

This can overflow in that multiplication in cases where your version would not, but if you are worried about that you can use the gcf function to cast out common factors between i and c, and between i and (n+1-i) before multiplying, just like in your Fraction.times function. This is a great point. ...
by jaap
Tue Jun 02, 2015 8:07 am UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 150207

Re: Project Euler

Anyone see any holes in it? :) Not really. There are a few minor stylistic issues: a = 0-a; might as well be a = -a; , and I'd prefer that kind of statement to numerator *= -1; but those are just quibbles. You could also use a=Math.Abs(a); instead of if (a < 0) { a = 0-a; } . There really is no nee...
by jaap
Tue Jun 02, 2015 5:38 am UTC
Forum: Logic Puzzles
Topic: What number pen ??
Replies: 9
Views: 3156

Re: What number pen ??

Vytron wrote:
Spoiler:
Qaanol wrote:And why on earth is pen 4 still empty? I though we agreed to put the RIVER OTTER in there, but it looks like someone put it in pen 6


Okay, I'm puzzled by this, why is RIVER OTTER in 6 and not 4? I thought it was in 4.


Spoiler:
How else does the ARCTIC FOX get to be in pen number 211?
by jaap
Mon May 25, 2015 9:25 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 461159

Re: Favorite math jokes

I used to have a teacher in primary school that gave NP's for good work (nearly perfect) because nothing was ever perfect. Is there a joke here? I believe the joke would be that the teacher put "NP" when the student got all the correct answers, whereas in such a circumstance a...
by jaap
Fri May 22, 2015 12:57 pm UTC
Forum: Science
Topic: Bladeless Wind Turbine: Do joints look better than fans?
Replies: 17
Views: 3275

Re: Bladeless Wind Turbine: Do joints look better than fans?

Question: can it still be used during storms or heavy gusts? If so: big win for the windpole. Wind turbines have to stop during bad weather to prevent them from taking damage. I am not an engineer, but I'd have to say/guess yes, simply because there are no moving parts. There is nothing to turn off...
by jaap
Wed May 20, 2015 3:11 pm UTC
Forum: Logic Puzzles
Topic: Tricky geometric proof
Replies: 8
Views: 5697

Re: Tricky geometric proof

SPACKlick wrote:Your given has some display issues, could you reframe it in words?

Sandor's picture has all the info in. I couldn't see some of the characters in the OP either, but it was fairly easy to deduce they must have been the symbol for perpendicular, but that has now all been captured in Sandor's picture.
by jaap
Mon May 11, 2015 12:24 pm UTC
Forum: Science
Topic: reducing joules to elementary units
Replies: 5
Views: 1310

Re: reducing joules to elementary units

kinetic energy is 1/2 mass * velocity^2, or 1/2 kilograms * meters^2/seconds^2 wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg+m%5E2+%2F+s%5E2+in+joules except... where did the 1/2 term go? what happened to the coefficient? You are mixing up units and measurements expressed in those u...
by jaap
Sat May 02, 2015 7:56 pm UTC
Forum: Mathematics
Topic: Equations Like f(2x)=4f(x)
Replies: 8
Views: 4592

Re: Equations Like f(2x)=4f(x)

1. f'(x) = f(f(x)) These are called idempotent functions, and they're pretty important in linear algebra. Let y be a point in the range of f. Then there is an x in the domain such that f(x)=y. Then the idempotent condition means that y = f(y). Since y was an arbitrary member of the range, it follow...
by jaap
Mon Apr 27, 2015 5:30 pm UTC
Forum: Logic Puzzles
Topic: Can you solve this?
Replies: 3
Views: 4161

Re: Can you solve this?

It is pretty easy to solve using one of those online substitution cipher tools that gives you the letter frequencies and performs the substitutions you choose. The only tricky bit is the figuring out what the letter c should be, as that is not a normal word. darkness, entropy, time, transposition: t...
by jaap
Sun Apr 26, 2015 10:37 am UTC
Forum: Mathematics
Topic: Tetrahedron with equal heights.
Replies: 1
Views: 1098

Re: Tetrahedron with equal heights.

No. As the tetrahedron has a well-defined single volume, and its volume equals a third the height times the base, it follows that all four faces have the same area. One easy way to ensure all faces have the same area is to use four faces of the same shape. You can for example use the tetrahedron wit...
by jaap
Fri Apr 24, 2015 11:06 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 2373

Re: Real roots of polynomials with integer coefficients

Is there a way to tell whether a polynomial has a multiple root without actually extracting the roots? Yes. If p(x) is the polynomial, then take its derivative p'(x), and then calculate gcd(p(x),p'(x)). If p has a multiple root, then that root will be shared with its derivative, and so this gcd wil...
by jaap
Thu Apr 23, 2015 3:40 pm UTC
Forum: Science
Topic: On friction
Replies: 17
Views: 3475

Re: On friction

You have the mass. That's all you need to find the force of gravity. Once you have that you can find the normal force. Once you have that you can find the force of friction. Once you have that you can calculate acceleration (or deceleration). Once you have that, everything else is easy! Nope, I hav...
by jaap
Tue Apr 21, 2015 8:45 am UTC
Forum: Mathematics
Topic: how to maximize number of beard states?
Replies: 8
Views: 2383

Re: how to maximize number of beard states?

The facial hair styles form a partial order . If style A shaved down into style B, you can say that A>B. There are pairs of styles that are not comparable, i.e. neither can be turned into the other because they both have some hair that the other doesn't. You can draw a graph, like the ones shown on ...
by jaap
Sat Apr 18, 2015 8:16 am UTC
Forum: Logic Puzzles
Topic: forget Cheryl's Birthday
Replies: 1
Views: 1887

Re: forget Cheryl's Birthday

We've had versions of this puzzle lots of times before: http://forums.xkcd.com/viewtopic.php?f=3&t=131 http://forums.xkcd.com/viewtopic.php?f=3&t=9308 http://forums.xkcd.com/viewtopic.php?f=3&t=45733 http://forums.xkcd.com/viewtopic.php?f=3&t=65980 http://forums.xkcd.com/viewtopic.ph...
by jaap
Wed Apr 15, 2015 3:29 pm UTC
Forum: Science
Topic: Earth's trajectory if the sun disappeared...?
Replies: 48
Views: 8904

Re: Earth's trajectory if the sun disappeared...?

I once did that same calculation for the moon (i.e. take twice the gravitational force it exerts to get the difference between when it's overhead and when it is opposite). This was in order to show that it would have virtually no effect on the blood circulation of a human being. It indeed wouldn't (...
by jaap
Wed Apr 15, 2015 9:48 am UTC
Forum: Logic Puzzles
Topic: Cheryl's Birthday
Replies: 29
Views: 6022

Re: Cheryl's Birthday

A slight tangent to the original question, but I know that the problem is asking what Cheryl's birthday is based on you being an outside observer to the problem. I was wondering if there's a way to work out how Albert was able to know the date based on him knowing that Bernard now knows the date. A...
by jaap
Thu Apr 02, 2015 7:37 am UTC
Forum: Logic Puzzles
Topic: Demonstrating objects are of equal weight
Replies: 12
Views: 4758

Re: Demonstrating objects are of equal weight

Zero. The problem can be solved without using a balance scale at all. 1. Weigh all the objects on a digital scale of sufficient precision and accuracy. 2. Weigh a single object on the same digital scale. 3. Divide the results. If the quotient equals the number of objects—meaning in particular it is...
by jaap
Tue Mar 31, 2015 5:04 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 120944

Re: Math: Fleeting Thoughts

Someone recently showed me a number (which I don't recall off the top of my head) which when multiplied by 2 or multiplied by 3 resulted in all the same digits, just rearranged. Is there a name for numbers with that property? Is there anything fancy being done 'under the hood' that makes numbers li...
by jaap
Tue Mar 24, 2015 12:34 pm UTC
Forum: Fictional Science
Topic: Super-Powers (Super-Speed!)
Replies: 73
Views: 15195

Re: Super-Powers (Super-Speed!)

Wait, is this true? If she's slowing time down, that means wavelengths will get longer; visible light would 'lengthen' into UV, and shorter wavelengths (like IR) would 'lengthen' into the visible spectrum. Unless I'm misunderstanding something? Infrared has a longer wavelength (lower frequency) tha...
by jaap
Thu Mar 19, 2015 10:28 am UTC
Forum: Mathematics
Topic: Probability of K sequence of X heads out of N coin flips
Replies: 6
Views: 1788

Re: Probability of K sequence of X heads out of N coin flips

This is typically a problem where the Inclusion-Exclusion Principle comes into play. To be honest however, I would not even attempt to do this in this manner, because there is a complication that hasn't been pointed out yet. The K sequences of X heads and their tail separators don't always take up t...

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