Let us imagine that we have a finite set 
Left: a set P of points in the real plane. Right: The span s is the maximum distance between two points of P.
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Archive for August, 2020
Jung’s Theorem: Enclosing a Set of Points
Published August 27, 2020 Occasional ClosedTags: Geometry
Left: a set P of points in the real plane. Right: The span s is the maximum distance between two points of P.
Is There Anyone Out There? The Drake Equation gives a Clue
Published August 20, 2020 Irish Times ClosedTags: Astronomy
The Drake Equation is a formula for the number of developed civilizations in our galaxy, the Milky Way. This number is determined by seven factors. Some are known with good accuracy but the values of most are quite uncertain. It is a simple equation comprising seven terms multiplied together [TM193 or search for “thatsmaths” at irishtimes.com].
A plaque commemorating the first appearance of the Drake Equation at a conference at the National Radio Astronomy Observatory, Green Bank, West Virginia in 1961.
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Think of a Number: What are the Odds that it is Even?
Published August 13, 2020 Occasional ClosedTags: Number Theory, Probability
Pick a positive integer at random. What is the chance of it being 100? What or the odds that it is even? What is the likelihood that it is prime?
Probability distribution 
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Resolution of Paradox: a Gateway to Mathematical Progress
Published August 6, 2020 Occasional Closed
Hermann Weyl (1885-1955)
A paradox is a statement that appears to contradict itself, or that is counter-intuitive. The analysis of paradoxes has led to profound developments in mathematics and logic. One of the richest sources of paradox is the concept of infinity. Hermann Weyl, one of the most brilliant mathematicians of the twentieth century, defined mathematics as “the science of the infinite” [TM192 or search for “thatsmaths” at irishtimes.com].
Ever since there has been time to wonder, humankind has been intrigued by the enigma of infinity. The idea has perplexed philosophers and mystified mathematicians for millennia. The Greeks were contemplating infinity from the time of Pythagoras. Head-on confrontation of infinity led to contradictory conclusions; the paradoxes of Zeno are amongst the most noted of these.
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