Symmetry & Fibonnaci

the quality of being made up of exactly similar parts facing each other or around an axis; a type of invariance: an object does not change even after undergoing a transformation

Symmetry

What are three types of symmetry?

• Bilateral symmetry or reflection symmetry

• Radial symmetry or Rotations

• Translations

object has two sides that are mirror images of each other

Bilateral symmetry or reflection symmetry

there is a center and numerous lines of symmetry can be drawn from the center

Radial symmetry or Rotations

when units are repeated and turn out having identical figures

Translations

What type of symmetry is this?

Translations

What type of symmetry is this?

Radial Symmetry

What type of symmetry is this?

Bilateral Symmetry

known as Fibonacci

Leonardo Pisano/Leonardo of Pisa

Who started questionning sequence thru this?

“How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?”

Leonardo Pisano/Leonardo of Pisa

Pineapples, pinecones, and sunflowers are examples of a Fibonacci sequence: True or false?

true

that the ratio between consecutive terms tends to converge to the number 1.61803399...

Golden Ratio

denoted by Φ

Golden Ratio

also called the divine proportion, golden mean, or golden section

Φ

true or false: Two quantities are in the golden ratio if their ratio is not the same as the ratio of their sum to the larger of the two quantities

False: their ratio should be the same as the ratio of their sum

the equation for Golden ratio

a and b, a > b >

What is this called?

Golden rectangle

What is this called?

Golden rectangle

Is it true that we can have the perfect ratio if we use golden ratio?

True

Starting with an isosceles triangle with base angles of 72°, bisecting one of the base angles gives another golden triangle.

Golden Triangle

What do you call when we get Whirling Triangles and a logarithmic spiral obtained by drawing arcs on one of the congruent sides.

Golden Triangle