Front Page, Interactive Mathematics Miscellany and Puzzles Since May 6, 1997You are visitor number 27862784 in base 11 The heart of mathematics consists of concrete examples and concrete problems. P.R.Halmos, How to Write MathematicsAMS, 1973 Also, some pages are organized into series while others, especially the older ones, are accessible individually. Throughout the discussions at this site I refer to various titles I love and find useful enough to have them in my own library. First off, you may want to look at the page that explains to the curious the origin and nature of my logo. There is also a page where I offer a beautiful geometric problem. One page currently presents 118 different proofs of the Pythagorean Theorem which was a great fun putting together. Another page looks into different ways a specific statement may be related to a more general one. Other pages have educational content. To me Internet is one of life's wonders. Recently I discovered the source of the 4 Travelers problem. |Contents||Store|

Optical Illusions and Visual Phenomena 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 .

Algebra: Themes, Tools, Concepts - Henri Picciotto Lucia de B. is innocent This internet site has been created by a group of individuals who form the “Committee for Lucia”. None of its members are related to Lucia, nor are they from her circle of friends. They are merely individuals driven by the certainty that Lucia is the victim of a gross miscarriage of justice. # News: BBC 23-7-2010 – Can chance make you a killer? Richard Gill 18-4-2010 – Bureau of Lost Causes This organisation has been set up inspired by the self-less efforts by so many people over the last six years, which only just now led to the extraordinary and total rehabilitation of Lucia de Berk. Guardian 14-4-2010 – Dutch nurse acquitted of being a mass murderer The ruling ended a bizarre legal odyssey during which the country's judicial system – right up to the Supreme Court – interpreted evidence wrongly, including statistics, autopsy results, and the nurse's diaries. The Independent 10-4-2010 – Nigel Hawkes: Did statistics damn Lucia de Berk? Google "Lucia" Trends # A gross miscarriage link or

Interactive GeoGebra Student Worksheet on Triangle Centers | {Eggsperimental Design} Geometry teachers! This is for you! Explore this wonderfully color-coded interactive diagram with your students. Enjoy my hard work!!! To create your own interactive triangle centers GeoGebra file, use the directions in the Google Docs document below. Preview is below. Emilie earned her Bachelors of Science in Mathematics at the University of Houston-Victoria. 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(, .

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?

Can Math Make a Better Marathon? Less than two miles from the finish of last month’s Chicago Marathon, with the race finally narrowed to a neck-and-neck duel between two Kenyan runners, the NBC television commentators began placing their bets. It wasn’t a hard call. Abel Kirui, who hadn’t won a marathon since 2011, was visibly struggling, repeatedly falling behind and then clawing his way back. At one point, grimacing, he snatched a cup of water from a volunteer and dumped it over his head. Such moments are what make marathons fascinating to watch and their results impossible to predict. In theory, the pace that a runner can sustain in a marathon is a straightforward function of physiology—how well the heart can pump fresh blood through the arteries, how much energy the leg muscles burn, and so on. Noakes is now most famous for having abandoned the idea of physiological limits entirely. At the moment, the clearest example of the potential impact of real-time data comes from cycling.

Desmos Grapher Untitled Graph Create AccountorSign In powered by powered by functions $$π Create AccountorSign In to save your graphs! + New Blank Graph Examples Lines: Slope Intercept Form example Lines: Point Slope Form example Lines: Two Point Form example Parabolas: Standard Form example Parabolas: Vertex Form example Parabolas: Standard Form + Tangent example Trigonometry: Period and Amplitude example Trigonometry: Phase example Trigonometry: Wave Interference example Trigonometry: Unit Circle example Conic Sections: Circle example Conic Sections: Parabola and Focus example Conic Sections: Ellipse with Foci example Conic Sections: Hyperbola example Polar: Rose example Polar: Logarithmic Spiral example Polar: Limacon example Polar: Conic Sections example Parametric: Introduction example Parametric: Cycloid example Transformations: Translating a Function example Transformations: Scaling a Function example Transformations: Inverse of a Function example Statistics: Linear Regression example Statistics: Anscomb's Quartet example

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.

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.

Imagining the 4th Dimension | IB Maths Resources from British International School Phuket Imagining the 4th Dimension Imagining extra dimensions is a fantastic ToK topic – it is something which seems counter-intuitively false, something which we have no empirical evidence to support, and yet it is something which seems to fit the latest mathematical models on string theory (which requires 11 dimensions). Mathematical models have consistently been shown to be accurate in describing reality, but when they predict a reality that is outside our realm of experience then what should we believe? Our senses? Our intuition? Or the mathematical models? Carl Sagan produced a great introduction to the idea of extra dimensions based on the Flatland novel. Mobius strips are a good gateway into the weird world of topology – as they are 2D shapes with only 1 side. Next we can move onto the Hypercube (or Tesseract). The page allows you to model 1, then 2, then 3 dimensional traces – each time representing a higher dimensional cube. For a more involved discussion (it gets quite involved!)

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