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Manifesto. Interactive Mathematics Miscellany and Puzzles

Manifesto. Interactive Mathematics Miscellany and Puzzles

Calculating the Distance to the Horizon For Any Game Home Up Site Map Assumptions | Method 1 | Method 2 Method 1 | Method 2 This is all based on the assumption that the horizon is the point on the world's surface at which the line of sight of the viewer, whatever their height, becomes parallel (tangential) to the surface of the world, and meets the surface of the world (so that the viewer cannot see any further than it). Note that I do not mention units in any of the equations on this page. Assumptions | Method 2 For a right-angled triangle: Where: R is the longest side (the hypotenuse), x and y are the other two sides. Using this equation on the triangle in the figure above, the longest side is the radius of the planet plus the height of the observer (r + h) , and the other two sides are d and r . Or, re-arranged: Or: So the total distance to the horizon is given by: This equation will work for any size world, and any height of observer. Assumptions | Method 1 Back to My Roleplaying Page .

PlanetMath Algebra: Themes, Tools, Concepts - Henri Picciotto Mu-Ency -- The Encyclopedia of the Mandelbrot Set at MROB A second-order embedded Julia set This is a picture from the Mandelbrot Set, one of the most well-known fractal images in the world. (Click it for a larger version). Here are some entries from Mu-Ency: Mandelbrot Set: The mathematical definition. More Pictures: Some entries with pictures of parts of the Mandelbrot Set are: R2, Cusp, Embedded Julia set, 2-fold Embedded Julia set, 4-fold Embedded Julia set, Paramecia, R2.C(0), R2.C(1/3), R2.1/2.C(1/2), R2t series, Seahorse Valley, Delta Hausdorff Dimension, Exponential Map, Reverse Bifurcation. You can also look up specific terms in the index. Coordinates of the image above: Center: -1.769 110 375 463 767 385 + 0.009 020 388 228 023 440 i Width (and height): 0.000 000 000 000 000 160 Algorithm: distance estimator Iterations: 10000 An ASCII art Mandelbrot set: vL , '*m-` -m/**\a, ... _,/#, ]),., ., '#F-.F~*^' '`'*~*eae/: . -__/* '`_* )_. ic,_ ./- T\a 7F*-~~*a, /` dL \_,\F^ '\` .*` .,___\____._/*^* R2a .m~ ` ' :*r(, .

Encyclopedia of Mathemaics Math Delights - Coins in Twoland by Joshua Zucker, joshua.zucker at stanfordalumni dot org In Twoland, the only coins are the toonies: 1, 2, 4, 8, 16, 32, 64, 128, and so on. The law says you must always pay with exact change; only the banks are allowed to make change. In Twoville you must pay with zero, one, or two of each type of coin, never more than two. (If Twoville is too complicated for you, try Oneville where you can only pay with zero or one of each coin!) For instance, to pay 6 toonies, you could pay with: one 4 and one 2 (and zero 1s) one 4, zero 2s, and two 1s or two 2s and two 1s. You could describe the three legal ways to pay by writing them in English, as I just did. Another, shorter way to write the list of legal ways to pay might be like this: 110102 022 (or simply 22). Create a table with the list of ways to legally pay for items that cost 1 toonie, 2 tonnies, ..., 16 toonies in Twoville, remembering that you cannot use more than two of each coin. What about the amounts that are exactly one single coin?

Quaternion Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji History[edit] Quaternion plaque on Brougham (Broom) Bridge, Dublin, which says: Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplicationi2 = j2 = k2 = ijk = −1 & cut it on a stone of this bridge Quaternion algebra was introduced by Hamilton in 1843.[7] Important precursors to this work included Euler's four-square identity (1748) and Olinde Rodrigues' parameterization of general rotations by four parameters (1840), but neither of these writers treated the four-parameter rotations as an algebra.[8][9] Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900.[10][11] i2 = j2 = k2 = ijk = −1, into the stone of Brougham Bridge as he paused on it. On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T.

Interactive Mathematics New Math Game: Factor Dominoes! Lately I've been looking for different ways for my seven year old and I to conceptualize multiplication. As has happened many times before on our math journey, this graphic showed up at just the right time (albeit somewhat circuitously through the excellent influence of the Math Munch blog). My favorite thing about it is that it's not about numerals; when I look at factoring trees I can make some surface sense of them, but my mind goes numb pretty quickly. In this visualization, however, there is an incredible connection to shapes and grouping. Last night I printed out the graphic and left it advantageously on the kitchen counter. She wondered what it was about so we looked it over together. It's the geometry of the design that really shows the relationships between numbers. All our talking and looking got my mind spinning. I was about halfway through constructing the cards when my big AHA! As we went along I refined the language she needed to help her make her choices.

Book Recommendations - EFnetMath These are semi-official #math book recommendations for various topics. These are all personal recommendations of channel regulars. This means that given the collective experience of the channel, these are the books to read. General Interest These books are intended for a general audience. history/philosophy of math, 'how to solve it' The History of Calculus and Its Conceptual Development ( by Boyer A History of Mathematics ( by Boyer A Mathematician's Apology ( by Hardy Pre-College Mathematics This category is the catch-all for topics generally preceding calculus. Schaum's outlines -- I used various ones for college-level math and they were useful, and the calculus one below is well-recommended. The book Calculus the Easy Way ( by Downing is an easy and intuitive introduction to calculus. Algebra Algebraic Geometry

Einstein for Everyone - StumbleUpon Einstein for Everyone Nullarbor Press 2007revisions 2008, 2010, 2011, 2012, 2013 Copyright 2007, 2008, 2010, 2011, 2012, 2013 John D. Norton Published by Nullarbor Press, 500 Fifth Avenue, Pittsburgh, Pennsylvania 15260 with offices in Liberty Ave., Pittsburgh, Pennsylvania, 15222 All Rights Reserved John D. An advanced sequel is planned in this series:Einstein for Almost Everyone 2 4 6 8 9 7 5 3 1 ePrinted in the United States of America no trees were harmed web*bookTM This book is a continuing work in progress. January 1, 2015. Preface For over a decade I have taught an introductory, undergraduate class, "Einstein for Everyone," at the University of Pittsburgh to anyone interested enough to walk through door. With each new offering of the course, I had the chance to find out what content worked and which of my ever so clever pedagogical inventions were failures. At the same time, my lecture notes have evolved. This text owes a lot to many. i i i

Tri-Hexa-Flexagon « After Math 7 The flexagon is an entertaining paper toy that has some educational value. 1. What kind of triangles? 2. 3. 4. The pattern and instructions I’ve attached worked well with students. Some students will need help the first time they fold and open the flexagon. After doing the fold/open/flatten operation, rotate the flexagon one triangle and then you are ready for the next fold/open/flatten operation. For the first few times, it helps to go back over the folds after flattening. There are many websites, but this is a good one for starters. This Hexahexaflexagon Tour video shows how to operate a flexagon. Template: Instructions: 0_flexagon Like this: Like Loading...

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