For almost 350 years it was known that 1729 is the smallest integer which can be expressed as the sum of two positive cubes in two different ways. Motivated by a famous story involving Hardy and Ramanujan, a class of numbers called Taxicab Numbers has been defined: Taxicab(k, j, n) is the smallest number which can be expressed as the sum of j kth powers in n different ways. So, Taxicab(3, 2, 2)...

BACKGROUND Taxicab drivers historically have had one of the highest work-related homicide rates of any occupation. In 2010 the taxicab driver homicide rate was 7.4 per 100,000 drivers, compared to the overall rate of 0.37 per 100,000 workers. PURPOSE Evaluate the effectiveness of taxicab security cameras and partitions on citywide taxicab driver homicide rates. METHODS Taxicab driver homici...

The famous story of the number 1729, the smallest integer which can be expressed as the sum of two positive cubes in two different ways, motivated the introduction of Taxicab Numbers. The smallest number expressible as the sum of two cubes in n different ways is called Taxicab(n). So, Taxicab(2) = 1729. Further on, Taxicab(5) = 48988659276962496. Computing Taxicab(n) is challenging and interest...

This paper proposes the Fuzzy Logic Model for Location Decisions of Taxicab Stands (FMOTS), which is a decision support system for decision makers, who wish to alleviate taxicab stand complexity in the short to medium term. In this study, an integrated model of GIS and fuzzy logic for taxicab stand location decision is built. The location decisions of taxicab stands in Ankara (Turkey), where or...

PROBLEM The homicide rate of taxicab-industry is 20 times greater than that of all workers. A NIOSH study showed that cities with taxicab-security cameras experienced significant reduction in taxicab driver homicides. METHODS Minimum technical requirements and a standard test protocol for taxicab-security cameras for effective taxicab-facial identification were determined. The study took more...

Carpooling taxicab services hold the promise of providing additional transportation supply, especially in extreme weather or rush hour when regular taxicab services are insufficient. Although many recommendation systems about regular taxicab services have been proposed recently, little research, if any, has been done to assist passengers to find a successful taxicab ride with carpooling. In thi...

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...

Taxicab service plays a vital role in public transportation by offering passengers quick personalized destination service in a semiprivate and secure manner. Taxicabs cruise the road network looking for a fare at designated taxi stands or alongside the streets. However, this service is often inefficient due to a low ratio of live miles (miles with a fare) to cruising miles (miles without a fare...

A natural analogue to angles and trigonometry is developed in taxicab geometry. This structure is then analyzed to see which, if any, similar triangle relations hold. A nice application involving the use of parallax to determine the exact (taxicab) distance to an object is also discussed.

BACKGROUND Driving a taxicab remains one of the most dangerous occupations in the United States, with leading homicide rates. Although safety equipment designed to reduce robberies exists, it is not clear what effect it has on reducing taxicab driver homicides. FINDINGS Taxicab driver homicide crime reports for 1996 through 2010 were collected from 20 of the largest cities (>200,000) in the U...