HO MMW Lecture 2 -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.
Editor's Notes
- #3: 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: Have you ever thought about how nature likes to arrange itself in patterns in order to act efficiently? Nothing in nature happens without a reason, all of these patterns have an important reason to exist and they also happen to be beautiful to watch.
- #5: Symmetry exists in living things such as in insects, animals, plants, flowers and others. Animals have mainly bilateral or vertical symmetry, even leaves of plants and some flowers such as orchids.
- #6: The folks at UniLAD decided to find out using Photoshop.re shaped the same, both eyes are in the same position, both ears stick out the same way, etc. The photo on the right is what the celebrity actually looks like. The photo the left is what he/she would look like if both halves of his face were the same. https://awkward.com/12-celebrities-with-symmetrical-faces-will-weird-you-out/ Celebrities tend to be way more attractive than the Average Joe. The reason: well, it all may come down to science. Research shows that having a symmetrical, well-proportioned face puts you in a much stronger position to land, say, the cover of Vogue or even an Oscar. The following stars' mugs have become the subject of intense aesthetic study over the years, and here are the results.Read More: https://www.nickiswift.com/2418/celebs-scientifically-beautiful-faces/
- #7: 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.Read More: https://www.nickiswift.com/2418/celebs-scientifically-beautiful-faces/ https://www.nickiswift.com/2418/celebs-scientifically-beautiful-faces/
- #10: 2. 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. For example, a tree grows by repetitive branching. This same kind of branching can be seen in lightning bolts and the veins in your body. Examine a single fern or an aerial view of an entire river system and you’ll see fractal patterns.
- #11: Examples of spirals are pine cones, pineapples, hurricanes. The reason for why plants use a spiral form is because they are constantly trying to grow but stay secure.