Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. The distance is positive if you ... A cab driver in New York picks up a passenger at Madison Square Garden and asks to travel to a theater which is four blocks north and two blocks east. We haven’t done a coding interview question for a while.

Obvious answer: segment. 32832 has 2 pairs found Messed up the links. A taxi cab company charges $8.00 per … in the Year 3000." The nice thing about this version is that it is possible to step up with x with a step of 2, as long you make sure that the sum of the triples of x and y are odd (even) if n is odd (even). { 87539319 [(167, 436), (228, 423), (255, 414)] 2004; right figure). Join the initiative for modernizing math education. He went into the room where Ramanujan was lying.

Snow, C. P. Foreword to A Mathematician's Apology, reprinted with a foreword by C. P. Snow public static void isTaxicabNumber(int inputNumber, int order) Godfrey Hardy was a professor of mathematics at Cambridge University. System.out.println(inputNumber +" is a Taxicab Number. When Ramanujan heard that Hardy had come in a taxi he asked him what the number of the taxi was.

When a particular number is multiplied thrice by itself the answer is called a “cube”, e.g. Compute and display the lowest 25 taxicab numbers (in numeric order, and in a human-readable format). Math.

Meyrignac, J. This is rather a brute force solution, but it manages to get Ta(4) in 19.5 minutes (searching to 7000000000000) while staying at a constant ~3.3GB of memory. Change ), You are commenting using your Facebook account. Indeed, 103 + 93 = 123 + 13 = 1729. ( Log Out /  Here’s a PHP script that checks all the numbers up to 2000 thus confirming the postulation. Whoops! 9, 1196-1203, 2003. https://www.cs.auckland.ac.nz/~cristian/taxicab.pdf. https://www.durangobill.com/Ramanujan.html. This property of 1729 was mentioned by the character Robert the sometimes insane mathematician, played by Anthony Hopkins, in the 2005 film Proof. This gives the resuls below in a few seconds.

An Introduction to the Theory of Numbers, 5th ed. Soc. Ta(5), […] Determine if a positive number can be expressed as a sum of two cubes? 39312 has 2 pairs found 2008. https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0803&L=nmbrthry&T=0&F=&S=&P=1059. The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes.

143604279 [(111, 522), (359, 460), (408, 423)] Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Problems in Number Theory, 2nd ed. Practice online or make a printable study sheet. Also I created a fast method to count triples, based on David Wilson’s page on Taxicab numbers and used it to generate numbers with 4 triples using his combination and magnification methods. Taxi-cab numbers, among the most beloved integers in math, trace their origins to 1918 and what seemed like a casual insight by the Indian genius Srinivasa Ramanujan. ( Log Out /  53, 778-780, 1957. Here’s one that is supposedly asked at Google: The mathematician G. H. Hardy was on his way to visit his collaborator Srinivasa Ramanujan who was in the hospital. Integer Sequences 2, #99.1.9, 1999. Dropping the segment size can make it use much less memory at a little speed expense. My Haskell solution (see http://bonsaicode.wordpress.com/2012/11/09/programming-praxis-taxicab-numbers/ for a version with comments): My version in Python. Euler's Conjecture." 3x3x3=27, so the number 27 is a cube. I have to say I enjoy seing the Haskell solutions, as they’re remarkably concise.

[…]. Not.

Create a free website or blog at WordPress.com. Each case is equally probable. 1729 is sometimes called the “Hardy-Ramanujan number”. "What Is the Value of Taxicab(6)?" Here a method to generate the triples more in line with this exercise. https://mathworld.wolfram.com/TaxicabNumber.html. Comp.

which is associated with a story told about Ramanujan by G. H. Hardy (Hofstadter 1989, Kanigel 1991, Snow 1993).

Knowledge-based programming for everyone. Hardy, always inept about introducing a conversation, said, … of Integer Sequences.". in a Christmas card in the episode Xmas Story (Volume 2 DVD, Georgoulias et Math. (by G. H. Hardy). String s; for ( int i = 1; i inputNumber) Sci. 27+8=35, so 35 is the “sum of two cubes” (“. ... (OEIS A011541). New York: Vintage Books, p. 564, The th taxicab number is the smallest break; J. 175959000 [(70, 560), (198, 552), (315, 525)] Sloane defines a slightly different type of taxicab numbers, namely numbers which are sums of two cubes in two or more ways, the first few of which are 1729, 4104, Pair :(" +i+","+j+")"); Greenwald, S. "Dr. Sarah's Futurama --Mathematics Kanigel, R. The Man Who Knew Infinity: A Life of the Genius Ramanujan. To this, Ramanujan replied that 1729 was a very interesting number — it was the smallest number expressible as the sum of cubes of two numbers in two different ways. Inst. So 1+1728=1729 Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Problems in Number Theory, 2nd ed. Silverman, J. H. "Taxicabs and Sums of Two Cubes." Leech (1957) found. 4, 181-184, 1995. {

(run* [q] (fresh [a ac b bc] (infd a b (interval 1 (int (java.lang.Math/cbrt n)) )) (infd ac bc (interval 0 n)) (cubo a ac) (cubo b bc) (+fd ac bc n) (== q [a b])))).

This one precomputes cubes and cube roots of interest, but only calls math.pow() once. 2004. He explained that it was the smallest number that could be expressed by the sum of two cubes in two different ways. To this, Ramanujan replied that 1729 was a very interesting number — it was the smallest number expressible as the sum of cubes of two numbers in two different ways. S.; Calude, E.; and Dinneen, M. J. Monthly 100, 645-656, 1993. https://euler.free.fr/taxicab.htm. Math Horizons, 12-15, Apr. Season 2 of the animated television series Futurama episode DVD 2ACV02 (Greenwald;

Indeed, 10 3 + 9 3 = 12 3 + 1 3 = 1729.

Still too slow for practically looking for larger values, but far, far faster than what I started out with.

Res. Your task is to write a function that returns all the ways a number can be written as the sum of two non-negative cubes; use it to verify the truth of Ramanujan’s statement.

A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer.

Maybe a topic for a next exercise? Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. 20683 has 2 pairs found A taxicab number is the name given by mathematicians to a series of special numbers: 2, 1729 etc. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Cambridge Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Washington

( Log Out /  Like danaj I created a segmented version of my first entry.



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