**'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.

**Link to**

The square root of minus
one

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".

and

Part II - An unsuccessful
attempt to express sin(10).

and

Part III - A proof that sin(10)
must be irrational.

__Cultural Souls
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
Rubik's Cube

Level 2 involves scrambling it just with 180-degree turns. Techniques
learned there, remain useful when tackling a completely mixed up puzzle.

Correspondence

Various calendars; Complex Numbers in Four Dimensions; Assessing Astrology;
Lunar resonances; Speed of Light from the Qur'an?

E-mail: __DLMcN@yahoo.com__