# Swannies Theorems, Art in Maths and a follow-up to Pythagoras, De Tinseau and De Gua De Malves.

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## Potpourri

1. Above - Two up - Left: Regular balls and 'regular hexahedrons' to honour Plato. Centre:  Areas: 1 : 1:  1 : 1 :1 : 2 : 2
What theorem? Right: Near perfect 'Stonenoids' on top of a circular ellipsoid.
2.  Above - Left:  Do the colours still add up correctly? Centre:  From Xhosa country like the Ball in the story but used to be
used in a more dangerous game. Right:  This finely constructed granite panelled monument in Lennox Street Port Elizabeth
is the closest in kind, shape wise, to his his theorems models that Swannie has seen.
4.  Below -Left: About moons and squares, yellow:black:red ≈ 14:8:14 (Complete outer circle and put it in a square for
more ratios to be had.) Centre:  It leads to Art in red. Right: Only guess which colour is more or perhaps less.

j5.  Above - two up, left: The green Yangma.  Found this in an old maths book, where it was called  a
Yangma. One of the three identical parts of the cube  is shown slightly raised. The shapes also
appear  in Exercise 5.3 in S K Stein's Calculus and Analytic Geometry, 4th Edition, McGraw-Hill.
centre: A 'moons in  red' ceation.
right:
What a shape! (If you can't find anyone to boost your ego do it yourself - others
are perhaps just jealous!)  Of the 425 men that completed the  2012  Redhouse River Mile
(near Port Elizabeth) only two were over 70.  Swannies, now 75 also did it when he was 60
and is looking foreward to attempt it again if he turns 90-ty - but maybe this was his swan swim!

6.  Above - left: The Tree Man of PE: Chain saw art requires a balanced approach.
centre:  Trun(k?)ated,
right:   projected and
7.  On the left:  re-foliated, live art created.

8.   Below:  Perhaps you have not dealt with squares within circles within squares?
left: How may times, in area, is the red square bigger than the green square? (no calculation!)
Note, another square can  fit  in nicely in the open ring.
centre: A clue.
right:  Use  Pythagoras and r squared  to 'see' the area ratio between the two circles.

9.  Above: Left: With two squares, four oblongs
and eight triangles you build  a
decatesserahedron.
Centre: Octahedron
Right: Four each of three different
shapes  (a square and  two  different
diamonds/rhombi) makes a  dodecahedron.

10. On the left:  It begins , it happens/grows
and it ends.

On the right:   Near cuboid, near cone/hyper
boloid, near Lady Grey.  All built mainly with
SiO4 tetrahedrons and  bigger 'blocks' up to
Si6O18. (Dana's Textbook of  Mineralogy 1951)

Reference:
See Contributors under
Arty Models. Much about them on the
Net. / The Oxford Mathematics Study
Dictionary comes in handy. / On the
spot reference to text books.

11.  Another beginning to end story (for
any grannies that may be reading this):

On the left: In a baby show he won a second prize
for  girls  which, being honest,  his mom  declined
to accept.

Undermost/the End: Swan song comming up?
Hopefully not  Yet!
2012 addition: Squaring/ Moron? Next Page

ANTHING NEXT? - Not likely, but do read the following: The  Special Theory (with own diagrams of objects stretching and shrinking) was a pet subject of Swannie some years back. Herewith a rhyme on Einstein:
Press glorification, Public adoration for:-  facinating Fiction originated, by Formal Physics accommodated; 'Star Wars' credibly rated by Time elasticated; Light, his speed  invariable, venerated; Longer Life contemplated and  truly, a Religion generated.
The rhymer pleads very common common sense. This being a  little heretic effort, also to try and catch some shine from the Special gift to mankind. This many science writers succeeded with, with a multitude of softcover books on the most amazing implications of the theory. Q: Do the watches and  hearts of astronaughts, up there, tick slower?

2012: SEE  next page SQUARING.