zen.pdf

GE1707 Mathematics in our World Patterns in Nature What Are Patterns? All around us, we see a great diversity of living things, from the microscopi...

GE1707 Mathematics in our World Patterns in Nature What Are Patterns? All around us, we see a great diversity of living things, from the microscopic to the gigantic, from the simple to the complex, from bright colors to dull ones. One (1) of the most intriguing things we see in nature is patterns. We tend to think of patterns as sequences or designs that are orderly and that repeat. But we can also think of patterns as anything that is not random. For example, we recognize the spots on a giraffe as a pattern, but they are not regular, nor are any of the spots the same size or shape. However, other patterns are orderly, as is seen in the symmetry of a sea star or a snowflake. Types of Patterns Symmetry Symmetry is when different sides of something are alike. These reflections may be mirror images with only two sides like the two sides of our bodies, they may be symmetrical on several sides like the inside of an apple sliced in half, or they might be symmetrical on all sides like the different face of a cube. We understand symmetry quite well in living organisms because it is a function of their environment. In order to balance, we need to have a symmetrical body structure, so we don't fall over from the imbalanced weight. What we don't understand very well is symmetry in non-living things. Snowflakes have six-fold symmetry, but it is unclear why this occurs. Likewise, the splash from a water droplet is also symmetrical, and while beautiful, it is still somewhat of a mystery. Fractals & Spirals Fractals are the 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale. We see this type of pattern in trees, rivers, mountains, shells, clouds, leaves, lightning, and more. Spirals are another common pattern in nature that we see more often in living things. Think of the horns of a sheep, the shell of a nautilus, and the placement of leaves around a stem. A special type of spiral, the logarithmic spiral, is one (1) that gets smaller as it goes. We see this pattern in hurricanes, galaxies, and some seashells. Fibonacci Patterns You may have heard of the Fibonacci sequence, which is the sequence of numbers that goes 1, 1, 2, 3, 5, 8, 13, 21…and so on. Each number is the sum of the two numbers before it; for example, 1 + 1 = 2; 1 + 2 = 3; 3 + 5 = 8; etc. How does this work in nature? We see that some plants exhibit a Fibonacci pattern, like the branches of a tree. You start with the main branch at the bottom. It splits off so that you have two, and it splits off again so that you have 3, and so forth. The family tree within a honeybee colony also exhibits a Fibonacci pattern. The drone in the colony hatches from an unfertilized egg, so it only has one (1) parent (1, 1…). But it has two grandparents because the queens and workers who produce these eggs have two parents (1, 1, 2…). It, therefore, has three great-grandparents (1, 1, 2, 3…), and so on. The reasoning behind the Fibonacci sequence in nature may be one (1) of the least understood of all the patterns. Tessellations Tessellations are patterns that are formed by repeated cubes or tiles. These, too, can occur with both living and non-living things. 01 Handout 1 *Property of STI Page 1 of 2  GE1707 The Use of Mathematics Technology – Modern technology depends on basic research to advance. GPS devices must know the speed of light to work, and this value is determined by math and experimentation using statistics. 1. Predicting the Weather 9. Navigation 2. Internet and Phones 10. Speech Recognition 3. Computers 11. Braking the Enigma 4. Reading CDs and DVDs 12. Public Transportation 5. Public Key Cryptography 13. Computer Circuits 6. Satellite Navigation 14. Movie Graphics 7. Digital Music 15. Image Compression 8. Search Engines 16. Measuring Time Engineering – In engineering, math is used to design and develop new components or products, maintain operating components, model real-life situations for testing and learning purposes, as well as build and maintain structures. Math is a core component of every engineering field and is also widely used in research. 1. Construction 6. Computer Circuits 2. Automotive Design 7. Rockets and Satellites 3. Building Bridges 8. Microwaves 4. Robotics 9. Surveying 5. Roller Coaster Design Media – Mathematical concepts and themes can be found everywhere in the media. The range of ways that math is related to the media is quite broad, including the shape of a camera lens, proportion and scale for movie sets, and the convincing nature of numbers used in advertising. 1. Reading CDs and DVDs 4. Movie Graphics 2. Digital Music 5. Polling and Voting 3. Making Music 6. Music Shuffling Medicine and Health – Advanced medical devices rely on studies supported by statistics. Even consumer devices, such as smartphones and tablet computers, are sold only when surveys and other forms of customer feedback, which rely on math, predict that they are profitable. 1. MRI and Tomography 6. Pharmacy and Medicine 2. Neurology 7. Population Dynamics 3. Epidemics Analysis 8. Plastic Surgery 4. Crowd People 9. Counting Calories 5. Problem Solving Finance and Business – Business ownership requires more than skill in creating a product or talent at providing a service. Overseeing the finances of your company is key to survival and success. Understanding basic business math is necessary for profitable operations and accurate record keeping. 1. Supply Chains 6. Fraud Detection 2. Finance and Banking 7. Big Data 3. Gambling and Betting 8. Pricing Strategies 4. Insurance 9. Game Theory 5. Loans, Internet, Mortgages REFERENCES: Vila, C. (2008). Nature by Numbers. Retrieved from Vimeo: https://vimeo.com/9953368/ Friedl, S. (N.D.) Patterns in Nature: Definition & Examples. Retrieved from Study.com http://study.com/academy/lesson/patterns-in-nature-definition-examples.html/ Applications of Mathematics (N.D.) Retrieved from Mathigon: https://mathigon.org/applications#/ 01 Handout 1 *Property of STI Page 2 of 2