Table of Contents
Which number is known as taxicab number?
1729
1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan’s number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H.
Why is 1729 a special number?
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 – a cube of 10 is 1000 and a cube of 9 is 729; adding the two numbers results in 1729.
How many taxicab numbers are there?
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.
Is 9 a taxicab number?
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
Who is known as Prince of mathematics?
Born April 30th, 1777, in Brunswick (Germany), Karl Friedrich Gauss was perhaps one of the most influential mathematical minds in history. Sometimes called the “Prince of Mathematics”, he was noticed for his mathematical thinking at a very young age.
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 |
Why is Ramanujan famous?
An intuitive mathematical genius, Ramanujan’s discoveries have influenced several areas of mathematics, but he is probably most famous for his contributions to number theory and infinite series, among them fascinating formulas ( pdf ) that can be used to calculate digits of pi in unusual ways.
What is taxicab geometry used for?
Taxicab geometry can be used to assess the differences in discrete frequency distributions. For example, in RNA splicing positional distributions of hexamers, which plot the probability of each hexamer appearing at each given nucleotide near a splice site, can be compared with L1-distance.
What is the most famous taxicab number?
The most famous taxicab number is 1729 = Ta (2) = 1 3 + 12 3 = 9 3 + 10 3 . The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy:
What is the nth taxicab number?
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
What is the taxicab number of 1729?
Taxicab number. In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
What are the upper bounds of the taxicab problem?
For the following taxicab number upper bounds are known: A more restrictive taxicab problem requires that the taxicab number be cubefree, which means that it is not divisible by any cube other than 1 3. When a cubefree taxicab number T is written as T = x3 + y3, the numbers x and y must be relatively prime.