منابع مشابه
On Hunting for Taxicab Numbers
In this article, we make use of some known method to investigate some properties of the numbers represented as sums of two equal odd powers, i.e., the equation x + y = N for n ≥ 3. It was originated in developing algorithms to search new taxicab numbers (i.e., naturals that can be represented as a sum of positive cubes in many different ways) and to verify their minimality. We discuss propertie...
متن کاملPlane Isometries and the Complex Numbers
The length of a vector v = ( x y ) in R2 is || ( x y ) || = √ x2 + y2, and the distance between two vectors v and w is the length of their difference: ||v − w||. A function h : R2 → R2 is called an isometry when it preserves distances: ||h(v)− h(w)|| = ||v −w|| for all v and w in R2. Examples of isometries include translation by ( 1 −1/2 ) , a rotation by 40 degrees counterclockwise around the ...
متن کاملWaring's Problem, Taxicab Numbers, and Other Sums of Powers
1. Introduction. Many of the most perplexing problems in number theory arise from the interplay of addition and multiplication. One important class of such problems is those in which we ask which numbers can be expressed as sums of some numbers which are defined multiplicatively. Such classes of numbers include nth powers (in this paper, for any fixed n; in a more general treatment, n could als...
متن کاملNew Upper Bounds for Taxicab and Cabtaxi Numbers
Hardy was surprised by Ramanujan’s remark about a London taxi numbered 1729: “it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways”. In memory of this story, this number is now called Taxicab(2) = 1729 = 9 + 10 = 1 + 12, Taxicab(n) being the smallest number expressible in n ways as a sum of two cubes. We can generalize the problem by...
متن کاملTaxicab tipping and sunlight
Does the level of sunlight affect the tipping percentage in taxicab rides in New York City? We examined this question using data on 13.82 million cab rides from January to October in 2009 in New York City combined with data on hourly levels of solar radiation. We found a small but statistically significant positive relationship between sunlight and tipping, with an estimated tipping increase of...
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ژورنال
عنوان ژورنال: Mathematical Sciences and Applications E-Notes
سال: 2015
ISSN: 2147-6268
DOI: 10.36753/mathenot.421214