: About Me

Hi! Thanks for stopping by! Professionally I am a retired physicist (Ph.D. Physics, University of Illinois at U-C, 1980), as well as a Registered Patent Agent. I maintained an active research career for about 35 years concentrating on condensed matter physics, with excursions into relativity theory, organic chemistry, photonics, pharmacology, and quantum computing. I was also part of the team who found the cause of the Columbia shuttle disaster.

Among other activities, I practice patent law, and have worked as a jeweler, website developer, entrepreneur, and opera tenor. I'm currently living in New Mexico with my lovely wife Camilla.

Sciences > Mathematics Difference between rational and irrational numbers

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In a sense, the difference between rational and irrational numbers is a simple one:  a rational number can be expressed as the quotient of two integers, and an irrational number cannot.  For example, 10 3/16 can be written as 163/16.  What is not immediately clear is that there are numbers which cannot be so expressed. To show this, we will use the demonstration developed in the 5th century BC by Hippasus of Metapontum.  Hippasus was a follower of Pythagoras, who taught that all numbers were rational.  One story relates that the Pythagoreans were so incensed at thi...

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