Mathematics in our Modern World lecture 2

1. WELCOME

2. ROLES THAT MATHEMATICS PLAY IN OUR WORLD
A. Mathematics helps organize patterns and
regularities in our world like
B. Mathematics helps predict the behavior of
nature and phenomena in the world.

3. Patterns and Regularities
Mathematics is all around us. As we
discover more about our environment, we can
mathematically describe nature. The beauty of
a flower, the majestic tree, even the rock
formation exhibits nature’s sense of
symmetry.

4.  Types of Patterns
1. SYMMETRY – a sense of harmonious and beautiful
proportion of balance or an object is invariant to any
various transformations (reflection, rotation or scaling.)
a) Bilateral Symmetry
- a symmetry in which the left and right sides of the
organism can be divided into approximately mirror image
of each other along the midline.

5.  Types of Patterns
1. SYMMETRY – a sense of harmonious and beautiful
proportion of balance or an object is invariant to any
various transformations (reflection, rotation or scaling.)
a) Bilateral Symmetry
- a symmetry in which the left and right sides of the
organism can be divided into approximately mirror image
of each other along the midline.
The team at UniLAD used Photoshop and reshaped the face to make both eyes in the same position, both ears stick out the same way, etc. The photo on the right
reflects the celebrity's actual appearance. The photo on the left illustrates what he/she would look like if both halves of their face were symmetrical.

6. In 2013, Dr. Kendra Schmid developed a formula that measured a person's attractiveness based on 29
different points of the face, with symmetry, proportion and ratio playing a key role in Schmid's 1-10 scale.
According to The Huffington Post, Schmid's formula determined that actor Brad Pitt has an almost perfect-
looking face. The actor earned an astounding 9.67 out of a possible 10 points, which, duh. Close behind Pitt
on Schmid's scale were actors Ryan Gosling, George Clooney, and Ben Affleck, who earned 7.31, 6.77, and
6.55 points, respectively.
Brad Pitt
Ryan Gosling
Ben Affleck
George Clooney

7.  Types of Patterns
1. SYMMETRY
a) Bilateral Symmetry
b) Radial Symmetry (or rotational symmetry)
- a symmetry around a fixed point known as the center
and it can be classified as either cyclic or dihedral. Plants
often have radial or rotational symmetry, as to flowers and
some group of animals. A five-fold symmetry is found in
the echinoderms, the group in which includes starfish
(dihedral-D5 symmetry), sea urchins and sea lilies. Radial
symmetry suits organism like sea anemones whose adults
do not move and jellyfish (dihedral-D4 symmetry). Radial
symmetry is also evident in different kinds of flowers.

8.  Types of Patterns
1. SYMMETRY – a sense of harmonious and beautiful
proportion of balance or an object is invariant to any
various transformations (reflection, rotation or scaling.)
a) Bilateral Symmetry
b) Radial Symmetry (or rotational symmetry)

9.  Types of Patterns
1. SYMMETRY
2. FRACTALS
– a curve or geometric figure, each part of which has
the same statistical character as the whole. A fractal is a
never- ending pattern found in nature. The exact same shape
is replicated in a process called “self-similarity.” The pattern
repeats itself over and over again at different scales.

10.  Types of Patterns
1. SYMMETRY
2. FRACTALS
3. SPIRALS
- A logarithmic spiral or growth spiral is a self-similar
spiral curve which often appears in nature. It was first
describe by Rene Descartes and was later investigated by
Jacob Bernoulli. A spiral is a curved pattern that focuses on a
center point and a series of circular shapes that revolve
around it.