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Gear300
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Who was it that associated n-tuples with vectors (was it originally Hamilton's work)?...or were n-tuples defined as a result of the attempt to define vectors?
N-tuples and vectors are mathematical objects that represent a set of numbers or values in a certain order. N-tuples are ordered collections of n elements, while vectors are quantities that have both magnitude and direction.
William Rowan Hamilton was an Irish mathematician who made significant contributions to the development of quaternions, a type of four-dimensional vector that extends the concept of complex numbers. Hamilton's work on quaternions led to advancements in the understanding of N-tuples and vectors.
The term "otherwise" is used to refer to the development of N-tuples and vectors by mathematicians other than Hamilton. This includes the work of mathematicians such as Gauss, Lagrange, and Einstein, who made significant contributions to the understanding of N-tuples and vectors.
N-tuples and vectors have a wide range of applications in science and engineering. They are used to represent physical quantities such as force, velocity, and acceleration in physics. In engineering, they are used to model and design complex systems, such as electrical circuits and mechanical structures.
The main difference between N-tuples and vectors is that N-tuples are ordered collections of elements, while vectors have both magnitude and direction. Additionally, N-tuples can have any number of elements, while vectors are typically represented by three-dimensional quantities in Cartesian coordinates.