It's a place full of wonder, strangeness and bizarre beauty: the room - or should I say space - of a mathematician that's merely a magician.

It's a common optical illusion, a kind of tricky paradox.

"If our brains are simple enough for us to understand them, then we'd be so simple that we couldn't." a Quote by Ian Steward (mathematician)

The floor itself is an impossible figure - a typical symbol for paradoxes... The spirals on the checkerboard-floor are Fibonacci spirals.

This drawing is mostly about the beauty of Phi Φ, Psi Ψ and the Fibonacci-sequence.

The fibonacci sequence works this way:

1+ 1 = 2

1+ 2 = 3

2+ 3 = 5

3+ 5 = 8

5+ 8 = 13

8+ 13 = 21

13+ 21 = 34

21+ 34 = 55

34+ 55 = 89

55+ 89...

...and so on...

The sequence then is: 1;1;2;3;5;8;13;21;34;55;89;...

Let's play with these numbers!

1/1=1

2/1=2

3/2=1.5

5/3=1.66666...

8/5=1.6

13/8=1.625

21/13=1.615384...

34/21=1.6190476...

...

If we continue this more and more, it will come closer and closer to a mathematical constant:

Phi Φ

By the way:

Φ=1.618033988749894848...

It can be calculated as followed:

Φ = (1+ √5) / 2

Psi Ψ

Psi is the golden angle. Its value is about 137.5°.

So... Let's connect Φ with π (Pi)

Ψ = 2π -2π+Φ = ~ 2.40 And now we show this as an angle:

2.40/2π = x/ 360°

(2π is the circumference of a circle (consider without r or r=1 ); 2Π is equal to a 360° circle: So 2.40 of 2π (It’s about 6.2831) is equal to x of 137.5°)

And here the x equals about 137.5°

2.40/ 2π = x/360° : And now we solve the equation for x → *360

x = 2.40/ 2π * 360 = 137.5

The golden angle can be found in nature in plants for instance. Did you ever wonder about the awesome arrangement of the blossoms’ leaves? Check out this picture:

Math can be really beautiful – Psi, Phi and Fibonacci show you one of the most awesome aspects of math!

This picture is dedicated to the beauty of mathematics, as well as the majesty of the Fibonacci-sequence, the golden ratio and the golden angle, which appear to be a sort of important algorithm in life.

Then there is the ghost again. It is a demonstration of a special figure-background relation.

The objects you can see below are a rolled-up one, a torus, a klein bottle and a hyperbolic paraboloid (or a saddle form).

© Dywiann Xyara 2018