The DW Math Thread

S> Refining luck. PM offers.

Only for you.


You should totally get a problem that's overly complex and full of useless information that has a solution so blindingly simple most wouldn't even consider it sometime. It'd be pretty amusing.

Mooooooooo - Lost City wrote: »

what is a cow + a duck?

b:chuckle pillow

more meth.

Decus - Dreamweaver wrote: »

三

The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?

thez harder b:shocked

maybe 468.

on

二. what do you mean moving in a vertical plane. liek gravity is only vertical?

Anyone can help me with this , f polinomial function in two variable X,Y , deg f =3 , from r^2 -->r , show that E:= [ (x,y) : F(x,y) is not 0 , so (x,y) is not a root , is not a conected space ] i think it has to do with the analytical propieties , and continues of polinomails in X,Y

Sorry for my english , i study in italian xD and tried to translate as i can

Decus - Dreamweaver wrote: »

The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?

2668 (unknown leg) and 3335 (hypotenuse)


Let integer sides = a, b, and h; let a = 2001; therefore, 2001 = a < b < h

Assumption: Pythagorean Triple (3,4,5); so a^2 + b^2 = h^2

Thus, using Euclid's Algorythm [gcd(a, b) = gcd(a, b - a) where b > a]; gcd = 667

More simply: 2001/3 = 667; 667 x 4 = 2668; and 667 x 5 = 3335

Therefore: b = 2668 and h = 3335

Test: 2001, 2668, 3335 is right-angled and is Pythagorean = 667 x [3, 4, 5]


I apologize for the clipped notation; I did this on an Excel spreadsheet; and, alas, I was but a poor History major. To be honest, I have a proclivity to view strings of numbers within the context of Fibonacci sequences (1,1,2,3,5,8 etc), or primes, and I write Haiku; so, my first instinct was to view 2001 and look for prime divisors. Three (3) became immediately apparent, and that caused me to think of the Pythagorean triplet -- 3,4,5. In essence, I solved the problem in under 30 seconds. The real problem was proving it; which, for an arithmatically handicapped being like me, was the real challenge.

Coincidentally, the relationship between Fibonacci numbers, right triangles, and Pythagorean triplets is also fascinating, but it was ultimately beyond my limited capacity to prove my results using Fibonacci, though I still think this is likely the most elegant solution to your problem.

Decus - Dreamweaver wrote: »

I am not really interested in elegant solutions, ...(

Had you seen my initial response, before I edited it several times, you would have seen a most inelegant solution. In high school I was selected as a semi finalist in a national math competition. My Trig teacher disqualified me because my solutions were completely unorthodox AND brutish. That accomplished two things: (1) a lifelong fear of math, and (2) a continual pursuit of the elegant solution.

During college I took a basic Art course, and when it came to perspective and distance, I found it a good deal simpler to convert by way of percentages, as opposed to the common practice of drawing endless horizon lines. My professor, who'd taught the course forever, had never seen such a thing.

When I still could, I used to sew occasionally and often found various equations handy, for instance, turning to Pythagoras when calculating needed yard goods. Also, I used to enjoy orienteering very much and Pythagoras became a constant friend when calculating distances on gridded maps.

Still fearful of mathmatics, but I do try to overcome it by way of everyday applications. Thank you for providing these problems.

I'm afraid I have to disqualify myself from the particle-vector problem. In researching, I stumbled across the source of your question and saw the equations you are seeking. b:cry

FayHumming - Dreamweaver wrote: »

b:chuckle 1 + 1 =

potato

*pokes*