# World's Hardest Easy Geometry Problem

5 Maths Gems #23 It seems like ages since my last gems post. School has been busier than I anticipated. This week I had reports to write and a Parents' Evening to attend - both tasks were particularly challenging because I've only been teaching these classes for a few weeks. I've also been marking at home every evening so it's hard to find time for Twitter and blogging. I have three other posts in draft - one about teaching quadratics, one about spontaneity and one featuring another batch of highlights from Chris Smith's newsletter back catalogue. So watch this space, they're all coming soon! 1. 2. My new favourite Twitter account is @etymathology. This week @BedtimeMath shared this fact about seconds, which I'd never heard before: It's funny how we can use a word like 'seconds' our whole lives and never give any thought to where it came from. And there you go - another example of Twitter's contribution to education. 3. 4. 5.

GSS - Circle through 3 points Drawing a circle through three given points with compass and straightedge 1. Draw the only circle that passes through the three points below. 2. Draw the only circle that passes through the three points below. (C) Copyright John Page 2007 Geometry Cool Free Online Math Games for Kids Play these Geometry Games to practice and reinforce your geometry skills the fun way. CCSS: 4.MD.C.5The balloons are coming in from all directions. Figure out the direction in degrees that the cannon needs to point and pop the balloons before they get too close. CCSS: 4.G.A.2, MP6MathPup is at Scruffy's Lab trying out his new device that can see outlines of shapes through steel. CCSS: 3.G.A.2Use your spacial reasoning skills and geometric knowledge to slice the geometric shapes into equal parts. CCSS: 3.G.A.2Finish Slice Geom? CCSS: 3.G.A.2The level pack to the great geometry game Slice Geom 2. CCSS: 4.G.A.1Match Geometry shapes to their name in this futuristic looking (and sounding) match game.

Evil Mad Scientist Laboratories - Iterative Algorithmic Plastic One of our favorite shapes is the Sierpinski triangle. In one sense, a mere mathematical abstraction, on the other, a pattern that naturally emerges in real life from several different simple algorithms. On paper, one can play the Chaos Game to generate the shape (or cheat and just use the java applet). You can also generate a Sierpinski triangle in what is perhaps a more obvious way: by exploiting its fractal self-similarity. Beginning with a single triangle, replace that triangle with three half-size copies arranged so that their outer border form a new triangle of the same size as the original. Then, replace each of those three triangles with three triangles half that size, and so forth. We begin with a few packages of polymer clay– two colors of Fimo Soft, in this case. Form the two clay colors into long triangular shapes. Press the stack of triangles together to make sure that the edges fuse well. Cut the stretched “first iteration” piece into four pieces of equal length.

5 Maths Gems #24 Hello and welcome to my 24th gems post - this is where I share 5 teaching ideas I've seen on Twitter. I'm going to be short and sweet today... I'm meant to be marking! 1. Angles in Parallel Lines I'm always on the look out for good questions that I can use in class so I was pleased when Cliff Pickover (@pickover) tweeted the problem below. 2. 3. 4.Circle Theorems Badges Cameron Fehr (@MrFehr_SVC) shared this picture of the circle theorem badges he uses to reward his students. Cameron made these himself using a badge maker. 5. 6. A bonus gem this week, especially for my American readers. Reading! Lucy Crehan (@lucy_crehan) shared this lovely post from the 'I am Malala' website. That's it for this week.

GSS - Constructions Introduction to constructions Constructions: The drawing of various shapes using only a pair of compasses and straightedge or ruler. No measurement of lengths or angles is allowed. The word construction in geometry has a very specific meaning: the drawing of geometric items such as lines and circles using only compasses and straightedge or ruler. Compasses Compasses are a drawing instrument used for drawing circles and arcs. This kind of compass has nothing to do with the kind used find the north direction when you are lost. Straightedge A straightedge is simply a guide for the pencil when drawing straight lines. Why we learn about constructions The Greeks formulated much of what we think of as geometry over 2000 years ago. Why did Euclid do it this way? Why didn't Euclid just measure things with a ruler and calculate lengths? One theory is the the Greeks could not easily do arithmetic. To find out more Constructions pages on this site Lines Angles Triangles Right triangles Triangle Centers

Geometry for Kids! The simplest geometric idea is the point, and then the line, the plane, and the solid. Shapes like circles, squares, rectangles, and triangles are flat, and we can think of them as being parts of a plane, flat like a drawing. Shapes like spheres, cubes, and pyramids are solid, and we can think of them as being part of the whole universe - as indeed any real object is. Pyramid When people work with geometric shapes, there are some things they often want to know about them. But how can we be sure that our ways of figuring the size of shapes are always going to work? Finally, we'd like to know how our ideas about shapes relate to our ideas about numbers. To find out more about geometry, check out these books from Amazon.com or from your library: Physics Chemistry Biology Science for Kids home page History for Kids home page Welcome to Kidipede! or *We don't use tracking and all ads are G-rated.

Magical Square Root Implementation In Quake III Any 3D engine draws it’s power and speed from the mathematical models and implementations within, and trust John Carmack of ID software for using really good hacks. As it turns out, a very interesting hack is used in Quake III to calculate an inverse square root. Preface ID software has recently released the source code of Quake III engine with a GPL license. In this article we’ll see Carmack work his black magic to calculate the square root of a floating point number blazingly fast. Carmack’s Unusual Inverse Square Root A fast glance at the file game/code/q_math.c reveals many interesting performance hacks. Observe the original function from q_math.c: float Q_rsqrt( float number ) { long i; float x2, y; const float threehalfs = 1.5F; x2 = number * 0.5F; y = number; i = * ( long * ) &y; // evil floating point bit level hacking i = 0x5f3759df - ( i >> 1 ); // what the fuck? In another file, code/common/cm_trace.c , a neater implementation of the same hack can be found. A Witchcraft Number

5 Maths Gems #26 Hello and welcome to my 26th maths gems - this is where I share teaching ideas and resources I've seen on Twitter. There's a lot going on this week - exciting times for maths teachers! Pi Day is fast approaching and it's a big one this year - 3.14.15. Speaking of number lines, this post about Open Number Lines by @mburnsmath is worth a read. Back to exercise books, I was really interested in @Ms_Kmp's post 'Indexed Learning' which is about students numbering every page in their exercise books. 2. I particularly like this question involving algebra - find the value of f. 3. I often write about Don Steward's resources - his website is wonderful. The 'reversing the question' activity below caused quite a stir on Twitter - it's a fantastic idea. Fawn Nguyen's post about her experience using this activity with her 6th graders (equivalent to Year 7) is worth reading. I like all the 'making up questions' material - here's another set of examples from Don's presentation: 4. 5.

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