DAVID McNAUGHTON: MATHEMATICAL TOPICS
'Phantom Forces' and 'Strange Numbers'
1. Architects in ancient civilisations could calculate static
forces quite accurately.
However, Dynamics remained undeveloped until about the 17th century AD. This particular science examines how forces affect moving objects. Special care is required if the environment (or reference-frame) is accelerating or spinning.
2. Even irrational numbers horrified many ancient Greeks, despite their prowess in mathematics.
When they discovered that the square root of two was irrational*, they thought they had stumbled upon a forbidden secret, thereby offending the Gods.
Hippasus of Metapontum was even expelled from the Pythagorean brotherhood for suggesting that they accept and try to work with irrational square roots. Some sources add that he was later shipwrecked and drowned.
What would those Greeks have said about people who used complex numbers? (Early Greek mathematicians did not even have a symbol for zero, let alone infinity).
*An irrational number is one which cannot be expressed as an exact quotient of integers.
The square root of minus
Not a normal number, but can still help to illustrate and calculate real physical changes
Dividing by zero
Infinity is also not an ordinary number; use it with caution
Centrifugal & Coriolis Effects
They are actually illusions, not genuine forces
The Laws of Multiplication
We are just lucky that 7 fives equal 5 sevens
Surd Expressions for Trigonometric Functions:
Part I - General discussion ... including sin 18º, along with other "curiosities".
Part II - An unsuccessful attempt to express sin(10).
Part III - A proof that sin(10) must be irrational.
reflected in their Mathematics: the Spenglerian interpretation
The mathematics developed in the Sino-Japanese High Culture focussed on solving some quite intriguing geometrical problems - ones which most Western mathematicians are completely unaware of. Other cultures, too, have displayed their own characteristic style and preferences in this field. Can we try and guess what type of mathematical thought might flower, in the future, in the recently born Russian Culture?
Scientific Culture, (Greece), January 2016, vol. 2 no. 1, pp. 1-6.
A three-stage process for mastering
Level 2 involves scrambling it just with 180-degree turns. Techniques learned there, remain useful when tackling a completely mixed up puzzle.
Various calendars; Complex Numbers in Four Dimensions; Assessing Astrology; Lunar resonances; Speed of Light from the Qur'an?
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