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Phi 1.618

Phi 1.618
ø PHI: The Golden Ratio or Golden Section (In Nature, Art, Science and Religion) The Golden Section is a unique Ratio (or relationship between parts) that seems to be preferred by Nature as the best geometry for growth, energy conservation, elegance and has some fundamental relationships to the platonic solids and the Mandelbrot set. It was formally discovered by the Greeks and incorporated into their art and architecture, but it has been shown to occur even in prehistoric art, possibly as a function of Man's natural affinity for it's beauty. The rectangle at left has a vertical edge length of 1 the horizontal or width of the rectangle is 1.618 If we make a line inside and form a square (far left) it creates another 'golden rectangle' (at right) this subdivision continues inward in a spiral fashion tracing the form of a perfect PHI spiral seen in galaxies, seashells .... Even your hand, arm, ear, teeth, etc are in PHI Proportions! Related:  math

Whatcom Community College :: Free Courses Online Math Center > Learning Math > Free Courses Free Courses Abstract Algebra Online This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra Abstract Algebra Study Guide Online notes written by John Beachy and William Blair for students using the textbook Abstract Algebra. Basic Math Review of basic math concepts produced by GCF Global Learning. Calculus on the Web "COW" @ Temple University COW is an internet utility for learning and practicing calculus. EdX: World-Wide University Open Coursework Free web-based publication of virtually all course content at over 30 acclaimed universities world-wide. Fractals: Cynthia Lanius´ Elementary/Middle School Intro A Fractals Unit for Elementary and Middle School Students Fractals: NWMI Mini Course Introduction to fractals written by Will and Rhonda Webber. Free Courses by Free-ed.net Free ed net: Prealgebra Mini-lessons, worksheets, extra practice on concepts from Prealgebra. KHAN Academy MathTV

How To Draw Daniel Kopsas Daniel Kopsas (pronounced "Copsis") E-mail: kopsasd@otc.edu Office Phone: (417) 447 - 8263 Twitter: I teach mathematics at Ozarks Technical Community College in Springfield, Missouri. I was inspired by Maria Andersen from Muskegon Community College to create this site and continue to pursue the use of technology in the mathematics classroom. For each of the courses in the sidebar to the left, I have built or I am currently building math video libraries. These libraries are constantly evolving and are not by any means perfect or completely error-free. If you are an instructor who would like to use some of my tutorials, and not necessarily send your students to this page to dig, there might be a simple solution. The tools I used to create the videos are a Wacom Bamboo tablet ($70), a Logitech USB headset ($35), and two free software packages: Jarnal (the handwriting software) and Jing or SnagIt (the screen recording software). Feel free to link to my page.

The Metric System The Metric System By the eighteenth century, dozens of different units of measurement were commonly used throughout the world. Length, for example, could be measured in feet, inches, miles, spans, cubits, hands, furlongs, palms, rods, chains, leagues, and more. The lack of common standards led to a lot of confusion and significant inefficiencies in trade between countries. The simplicity of the metric system stems from the fact that there is only one unit of measurement (or base unit) for each type of quantity measured (length, mass, etc.). To simplify things, very large and very small objects are expressed as multiples of ten of the base unit. Table 1: Common metric prefixes. The subunits are used when measuring very large or very small things. The metric system is a called a decimal-based system because it is based on multiples of ten. Because the metric system is based on multiples of ten, converting within the system is simple. Scientific notation Key Conceptstoggle-menu

OCSD Interactive Games Design Your Own Games Pre-Made Games Matching Game Directions- In this game you can match up words. You have two columns to work in . Type in your words in the first column and the matching words in the second column. Type in a Title for your game. Editing Your Matching Games If you need to edit your game open up the matching game and type in the filename in the box and then hit load. Term Matching Game- In this game you can put in terms and definitions. Type in a Title for your game. Graphic Matching Game- In this game you can match up words with graphics or use all graphics. Email me a page (either a web page or a word document) that has the images you want to use. Drag Matching Game Directions- In this game you can match up words by dragging them. Type in a Title for your game. Drag Term Matching Game- In this game you can put in terms and definitions. Type in a Title for your game. Quiz Time- This will allow you to create an interactive multiple choice quiz for your students.

The Secret to Teaching Math Facts: Number Bonds Below you will see why I think teaching math basics with number bonds is the best way for your homeschoolers to learn math. Over our last four years of homeschooling, I have used several different math curricula. Some I liked better the others, but they all had their own strengths and weaknesses. One of the strengths of one particular curriculum we use, Singapore Math, is their method of teaching basic math facts. Instead of teaching fact families by rote, Singapore illustrates fact families using number bonds. Now, I realize this is just my unprofessional opinion, but as a self-professed math geek, I truly believe number bonds are (likely) the best ways to teach math facts. Why? They're simple. How Number Bonds Work If you're not familiar with what number bonds are, allow me to illustrate. As in the example for addition on the left, the student is taught to recognize that the number 7 is made of 3 and 4. Number Bond Flashcards Teaching Algebraic Thinking

Adding Signed Numbers - Lesson 101 Video Adding Signed Numbers - Lesson 101 Hi, I’m Larry. This is the video from Lesson 101 on my website, adding signed numbers. This is one of the most important lessons on my site so make sure that you fully understand it and feel fully comfortable with it. I you have difficulty understanding this lesson you will have trouble with all the materials that follows because it builds up on this lesson especially when we get to Algebra we’re going to be using the skill again and again, so make sure that you don’t have any difficulty with it whatsoever. Up until now I’ve been working with adding positive numbers and we haven’t any trouble with that. Now, very often students say something like, “Wow! Now, I like to think of negative numbers as a debts or how much money I owe, so if I say negative three I’ll think of that as I owe $3.00. For this example I’d like to add 3 + -5. Here’s how I like to teach you. Okay, so the situation is I have $3.00 but I owe you $5.00.

Integer Number Line In this lesson,we will look at integers and the number line. Related Topics: More Lessons on Integers Integer Worksheets Integer Games Integers Integers consist of negative integers, zero and positive integers. Example: 0 is an integer but is neither positive nor negative. Negative numbers have a ‘–’ sign before them. Example: –3 is read as “negative three” +6 or 6 is read as “positive six” or “six” Opposite of a Number The opposite of a number is the number with the sign changed. The opposite of 4 is –4 The opposite of –6 is 6 Since 0 is neither positive nor negative, the opposite of 0 is also 0. Number Line Integers can be represented on the number line. An integer on the horizontal number line is greater than the number on its left and less than the number on its right. Example: –1 is greater than –2 and less than 0. We can also write it as –1 > –2 and –1 < 0. Recall that “>” means greater than and “<” means less than. On the number line, moving to the right is positive. OML Search

s Math Resources - Integers: Operations with Signed Numbers Have you ever been to a party like this? Everyone is happy and having a good time (they are ALL POSITIVE). Suddenly, who should appear but the GROUCH (ONE NEGATIVE)! The grouch goes around complaining to everyone about the food, the music, the room temperature, the other people.... What happens to the party? But wait... is that another guest arriving? What if another grouch (A SECOND NEGATIVE) appears? Now that the two grouches are together the rest of the people (who were really positive all along) become happy once again. The moral of the story is that (at least in math, when multiplying or dividing) the number of positives don't matter, but watch out for those negatives!! To determine whether the outcome will be positive or negative, count the number of negatives: If there are an even number of negatives -and you can put them in pairs- the answer will be positive, if not... it'll be negative: Negatives in PAIRS are POSITIVE; NOT in pairs, they're NEGATIVE.

The Thirty Greatest Mathematicians Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Please e-mail and tell me! Following are the top mathematicians in chronological (birth-year) order. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. Early Vedic mathematicians The greatest mathematics before the Golden Age of Greece was in India's early Vedic (Hindu) civilization. Top Thales of Miletus (ca 624 - 546 BC) Greek domain Apastambha (ca 630-560 BC) India Pythagoras of Samos (ca 578-505 BC) Greek domain Panini (of Shalatula) (ca 520-460 BC) Gandhara (India) Tiberius(?) Geocentrism vs.

Math Help An Engineers Quick References to Mathematics Algebra Help Math SheetThis algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples. There is a description of the quadratic equation as well as step by step instruction to complete the square.Download PDFDownload Image Geometry Math SheetThis geometry help reference sheet contains the circumference and area formulas for the following shapes: square, rectangle, circle, triangle, parallelogram, and trapezoid.

Tutorials Menu Note: Yo Quiero Math has a new site "Math Para Mi" at " All tutorials and any additional tutorials are being housed in this new site. Please click the link for Math Para Mi. Home Page What are Integers? An introduction to integers-- learning to compare integers. (Discusssion) What is the absolute value of an integer. Adding Integers on The Number Line (Discussion) Rules for adding Integers (Discussion) Subtracting Integers (Discussion) The Laws of Addition (Discussion) work Exercises 1. Work Exercises 2. Work Exercises 3 Practice Adding integers on the Number Line. Using rules to Add Integers Work Exercises 4 Using the number line and Rules to Subtract integers or Sign numbers Exercises 5 Practice your understanding of the laws of addition Exercises 6 Home Page

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