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TABLE OF CONTENTS
Title
Page
Who Is William Hamilton?
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Mathematical Discoveries
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And Accomplishments
Contribution To Technology 4
And The Field Of
Mathematics
Bibliography
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Who is William Hamilton?
William Rowan Hamilton was born on August 4, 1805. He was the fourth of nine
children who lived in Dublin, 38 Dominick Street. His father, Archibald Hamilton, worked as a
solicitor ( the chief law officer of a town of city ). His mother was Sarah Hutton. At a very young
age his father sent him to live with his uncle, James Hamilton. There his ability to learn
languages was discovered. He showed great understanding at this young age of the Hebrew,
Persian, Arabic, Hindustani, Latin, Greek, Syriac, French, Italian, Sanskrit, Marathi and Malay.
Most of them he understood before he was a teenager.
At the age of 9 he was place against Zerah Colburn in a mental arithmetic contest and
was defeated. This brought his attention to mathematics as he dedicated less time to studying
languages and more time on mathematics. He studied Languages and Mathematics even till his
days in college. He dedicated his life to mathematics and has made astonishing discoveries that
we still use today and maybe for the rest of our lives on earth. He became a well known Irish
physicist, astronomer and mathematician and contributed to our knowledge on optics ( branch of
physics that deals with the behavior and property of light ), algebra and classical mechanics. He
died at the age of 60 on September 2, 1865.
Mathematical Discoveries and Accomplishments
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He published a mathematics paper known now was he Theory of Systems of Rays. It
was first called the Caustics in 1824. This paper presented his discovery of proving that a system
of light rays filling a region of space can be focused down to a single point by a specific curved
mirror if and only if those light rays are orthogonal to some series of surfaces. The property can
be down under reflection in any number of mirrors. He followed up by a mathematical
investigation of the foci (center of interest or activity) and caustics of reflected light.
Later on while continuing to build on this theory and focus he created a single function
that brought together mechanics, optics and mathematics. This was known as Hamilton’s
Principal Function and helped to found the wave theory of light. He later developed a great
principle of Varying Action. It predicted that a single ray of light entering a biaxial crystal at a
certain angle would emerge as a hollow cone of rays. This is known as Conical Refraction.
Hamilton was an expert in arithmetic calculation. At the age of 12 he studied Newton’s
Arithmetica Universalism which was his introduction to modern analysis. He later began reading
the Principia which is the Mathematical Principles of Natural Philosophy. It is the work of Sir
Isaac Newton. At the age of 16 he was a master at it. He also mastered Analytical Geometry and
Differential Calculus. He then attended Trinity College in Dublin and furthered his studies.
He later discovered Quaternion in 1843. He came about this when he was looking for a
way to extend complex numbers which are usually viewed as 2-dimensional planes to a higher
spatial dimension. He did not find a 3-dimensional system but worked with four dimensions to
create quaternion. The idea came to him on a lovely walk with his wife on October 16. The
quaternion equation is i2 = j2 = k2 = ijk = -1. He described a quaternion as an ordered fourelement multiple of real number and described the first element as the scalar part and the
remaining three as vector parts. Hamilton introduced a method of analysis both quaternion and
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biquaternions. Biquaternions are the numbers w + xi + yj + zk, where w, x, y and z are complex
number and the elements of 1, i , j and k multiplied as in the quaternion group. This analysis is
the extension to eight dimensions by introduction of complex number coefficients.
Other Discoveries
Hamilton developed the Variational Principle which was revised by Carl Gustav Jacob Jacobi.
He also created the icosian game which can be solved using the concept of a Hamiltonian path.
Contributions to Technology and the Field of Mathematics
Hamilton’s quaternion has contributed to Technology as it is used in computer graphics. Control
theory, signal processing and orbital mechanics. Spacecraft attitude-control systems are often
commanded in terms of quaternion. His discoveries have built the world’s understanding of
Mathematics as well as Physics. He has contributed to my knowledge as well as the future
generations of the world. Hamilton is recognized as one of Ireland’s leading scientists.
Some definition of words and phrases that may be unclear:
● Computer Graphics- This is the representation of image data by a computer with the
help of a specialized graphic hardware and software. (Wikipedia)
● Control Theory- This is a branch of engineering and mathematics that deal with the
behavior of dynamical systems with inputs. (Wikipedia)
● Signal Processing- This is an area of systems and electrical engineering and applied
math which deals with operations on, analysis of signals or measurements of timevarying quantities. (Wikipedia)
● Orbital Mechanics- This is the application of ballistic and celestial mechanics to the
practical problems concerning the motion of rockets and other spacecrafts. (Wikipedia)
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BIBLIOGRAPHY
http://en.wikipedia.org/wiki/William_Rowan_Hamilton
http://www.britannica.com/EBchecked/topic/253431/Sir-William-Rowan-Hamilton
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