Why is 1729 called a taxi cab number?
Table of Contents
The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103. The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan.
What is a taxi number in math?
From Simple English Wikipedia, the free encyclopedia. A taxicab number is the name given by mathematicians to a sequence of special numbers: 2, 1729 etc. A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways.
What are the 6 taxicab numbers?
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, 13832, 20683, 32832, 39312, 40033, 46683, 64232, (OEIS A001235).
Is 4104 a taxicab number?
4104 (four thousand one hundred [and] four) is the natural number following 4103 and preceding 4105. It is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729, is called the “Ramanujan–Hardy number”….4104 (number)
| ← 4103 4104 4105 → | |
|---|---|
| Hexadecimal | 100816 |
Is 20683 a Hardy-Ramanujan number?
Ramanujan’s 2-way solution {1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763.}
Why is Ramanujan number 1729?
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.
Is 2 a Ramanujan number?
Ramanujan’s 1-way solution Integers that are expressed as the sum of 2 cubes (in at least one way). Some of these numbers include : {2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737.}
How do you check if a number is a Ramanujan number?
Ramanujan Numbers are the numbers that can be expressed as sum of two cubes in two different ways. Therefore, Ramanujan Number (N) = a3 + b3 = c3 + d3. Explanation: The number 1729 can be expressed as 123 + 13 and 103 + 93.
Is there any number like 1729?
“No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The two different ways are: 1729 = 13 + 123 = 93 + 10….1729 (number)
| ← 1728 1729 1730 → | |
|---|---|
| Divisors | 1, 7, 13, 19, 91, 133, 247, 1729 |
| Greek numeral | ,ΑΨΚΘ´ |
| Roman numeral | MDCCXXIX |
| Binary | 110110000012 |
Is 1458 a Ramanujan number?
Suppose, we want to check the number 1458 is a Ramanujan number or not. We get the same number that we have taken. Hence, the given number is a Ramanujan or taxicab number.
What number is Kaprekar?
6174 is known as Kaprekar’s constant after the Indian mathematician D. R. Kaprekar.