Fairy Lights on the Farey Tree. Parity types are coloured as follows: Even: Blue; Odd: Green; None: Red.
The rational numbers 
Archive for May, 2022
Image Processing Emerges from the Shadows
Published May 19, 2022 Irish Times ClosedTags: Astronomy, Trigonometry
Satellite images are of enormous importance in military contexts. A battery of mathematical and image-processing techniques allows us to extract information that can play a critical role in tactical planning and operations. The information in an image may not be immediately evident. For example, an overhead image gives no direct information about the height of buildings or industrial installations, but shadows, together with the time, date and basic trigonometry, enable heights to be determined [TM233 or search for “thatsmaths” at irishtimes.com].
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Parity and Partition of the Rational Numbers. Part II: Density of the Three Parity Classes
Published May 12, 2022 Occasional ClosedTags: Number Theory
In last week’s post, we defined an extension of parity from the integers to the rational numbers. Three parity classes were found — even, odd and none. This week, we show that, with an appropriate ordering or enumeration of the rationals, the three classes are not only equinumerate (having the same cardinality) but of equal density in
Parity and Partition of the Rational Numbers. Part I: The Three Parity Classes
Published May 5, 2022 Occasional ClosedTags: Number Theory
We define an extension of parity from the integers to the rational numbers. Three parity classes are found — even, odd and none. Using the 2-adic valuation, we partition the rationals into subgroups with a rich algebraic structure.
Continue reading ‘Parity and Partition of the Rational Numbers. Part I: The Three Parity Classes’
ThatsMaths 