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The Fibonacci Numbers and Golden section in Nature - 1

The Fibonacci Numbers and Golden section in Nature - 1
This page has been split into TWO PARTS. This, the first, looks at the Fibonacci numbers and why they appear in various "family trees" and patterns of spirals of leaves and seeds. The second page then examines why the golden section is used by nature in some detail, including animations of growing plants. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. 1 Rabbits, Cows and Bees Family Trees Let's look first at the Rabbit Puzzle that Fibonacci wrote about and then at two adaptations of it to make it more realistic. 1.1 Fibonacci's Rabbits The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. How many pairs will there be in one year? At the end of the first month, they mate, but there is still one only 1 pair. The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ... Related:  mathematics

Chaos & Fractals Chaos is a relatively new and exciting science. Although chaos was often unfavorably viewed its early stages, scientists now perform active research in many areas of the field. Presently, there are several journals dedicated solely to the study of chaos. This website was written in conjunction with a talk given for Intermediate Physics Seminar of the Department of Physics and Astronomy at the Johns Hopkins University. It is intended to merely highlight a few of the more interesting aspects in the field of chaos. For further information, please consult the reference section of this document.

What’s the Difference Between a MOOC and an LMS? | Your Training Edge ® Massive open online courses (MOOCs) have been around long enough that most people in the training industry have at least a general understanding of what they are. But there is still some confusion about how they differ from more familiar forms of elearning and online courses. In particular, a question I’m often asked is: “What’s the difference between a MOOC and a learning management system (LMS)?” The basic answer is that an LMS is a platform for hosting a course, while a MOOC is the course itself. In general, however, I don’t think the real question is about the difference between a MOOC as a course and an LMS as a platform. Small versus large (or massive) In theory MOOCs can accommodate an unlimited number of learners. Discrete versus continuous Traditional courses hosted on LMSs are usually discrete entities, meaning that that they start on a particular day, end on a particular day, have particular due dates, and so on. Content versus context This is a common distinction that is made.

library.thinkquest.org/3703/ As of July 1, 2013 ThinkQuest has been discontinued. We would like to thank everyone for being a part of the ThinkQuest global community: Students - For your limitless creativity and innovation, which inspires us all. Teachers - For your passion in guiding students on their quest. Partners - For your unwavering support and evangelism. Parents - For supporting the use of technology not only as an instrument of learning, but as a means of creating knowledge. We encourage everyone to continue to “Think, Create and Collaborate,” unleashing the power of technology to teach, share, and inspire. Best wishes, The Oracle Education Foundation Kidspiration - The Visual Way to Explore Words, Numbers and Concepts Created for primary learners, Kidspiration® develops literacy, numeracy and thinking skills using proven visual learning principles. In literacy, Kidspiration strengthens word recognition, vocabulary, comprehension and written expression. With new visual maths tools, students build reasoning and problem-solving skills. Kidspiration helps pupils: Develop strong thinking skills Strengthen literacy skills Build conceptual understanding in maths Develop Strong Thinking SkillsStrengthen Literacy SkillsBuild Conceptual Understanding in MathsEducator Developed Resources Support Curriculum IntegrationEasy Navigation and Simple Operations Support for Every Primary LearnerTeacher Options Keep Pupils Focused on LearningSupport for ELL and ESL StudentsKidspiration Keeps Up with the Latest Technology Kidspiration provides a cross-curricular visual workspace for primary learners. Kidspiration works the way pupils think and learn and the way teachers teach. Develop Strong Thinking Skills

Golden ratio Line segments in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.[1][2][3] Other names include extreme and mean ratio,[4] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8] Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Calculation Therefore, Multiplying by φ gives and History

Interactive Mathematics Miscellany <br>and Puzzles Podcasts and Downloads - More or Less: Behind the Stats 20 fun apps to put your students' smartphones to good use Sometimes your classroom lacks technology. You only have one computer or one iPad. You can get far with just that, but it would be nice sometimes to have a 1-to-1 classroom. Nowadays, almost every student beyond primary school has a smartphone. How to use smartphones in the classroom If you didn’t realize you could use smartphones for an educational purpose, you should keep reading. It’s easy to let your students use smartphones in your classroom, but it’s hard to keep them under control. Using smartphones apps in the classroom Let your students download a few of your favorite apps, and you’re ready to go. 1. Poll Everywhere is a voting system, completely reinvented! Questions can be polls, but also open ended questions like “give me a tip to improve my teaching”. Students can respond by using the web app, a text message via the Poll Everywhere smartphone app or even Twitter. Another fun feature is the ability to make nice charts of the answers. 2. 3. Want to give it a try? 4. 5. 6. 7. 8.

Divide By Zero About To Divide by Zero is an internet slang term describing an action that leads to an epic failure or theoretically unlikely disaster, such as an earth-shattering apocalypse or a wormhole in the time-space continuum. The concept of division by zero is also associated with the phrase “OH SHI-,” which represents the response of someone that is cut off mid-sentence as a result of the disaster. Origin The earliest known reference to division by zero can be found in a YTMND site titled “1/0 !!!!!!!!!!!!” However, according to Encyclopedia Dramatica, the phrase is said to have originated on 4chan’s /b/ (random) board, with its earliest dating to December 8th, 2006. In Mathematics In math with real numbers, values that represent quantities along a continuous line, division by zero is an undefined operation, meaning it is impossible to have a real number answer to the equation. Spread Mr. Notable Examples Search Interest External References

Stand up school Dr. Kirk Lewis High School (Houston, TX) Maximizing Space, Effort & Time "People tend to stay focused and more on task. - Jason Rhodes, 9th grade AP human/world geography teacher Read More Alexandria Country Day School (Alexandria, VA) Creating a Responsive Classroom Design "I really like how the desks help you think outside the box with teaching... not only does it engage the kids, it frees you to do whatever you need to do in your room when you can easily move everything around." - Monica Escobar, 6th grade language arts and history teacher Read More Montera Middle School (Oakland, CA) Always in Action, Always Engaged "Some students can sit for many hours and listen and focus - that’s great. - Ashanti B., Montera Middle School Principal

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