Check out the activity here! Also, visit NRich Math for a slightly different way to create designs from your times tables!
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Walk Through Paper Can you walk through a hole in an 8. Pass out a sheet of paper to all of your students and see if they can figure out how to cut a hole large enough for them to fit through. Then, show them this magical trick! Afterwards, stretch your paper out and try to find the area and perimeter of your paper! How did it change? For younger students, this project can tie into a basic measuring unit.
You can even fit through an index card! Click here for details! All they need is a set of dominoes! Click here for the full list! Check out domino magic squares and rectangles here! Then, they just subtract corner to corner. The big surprise is their final square! Like magic, all of the corners are the exact same numeral! Inference : See if kids can predict what will be their mystifying number before solving all their squares! Now I have this feeling that almost everything is unknown about mathematics.
I like things where I can just start working. I like to just get my hands dirty and start right away. One problem I got very interested in was the triangular billiards problem. It asks: If you look at billiards in a triangle, is there a periodic billiard path—one that traces the same path over and over again? The question is: Does every triangle have a periodic billiard path?
So I made some progress on this. I proved that as long as all the angles are less than degrees, there is a periodic billiard path.
Math Puzzles for Kids:
Could you give me another example? Another thing I worked on for quite a while and did solve is a problem in outer billiards. Here you have a convex shape in the plane, like an oval, square or pentagon. You start at a point outside the shape and you, well, maybe I should draw a picture of this.
20 Math Puzzles to Engage Your Students | Prodigy Math Blog
You start at your initial point, then draw a line that goes tangent to the shape—it touches the shape at a single point. Stop at a point equidistant to the tangent point from your original point. Then repeat the process to create something like an orbit. The main question all along was: Is there a shape and a starting point such that the point moves arbitrarily far from the shape?
Is the orbit unbounded?
I showed that for certain shapes—for kites, which are quadrilaterals with bilateral symmetry—you can escape. Mathematicians, even the old greats like Gauss and Euler, were trying to gather experimental evidence. In a sense, the computer lets you do a lot more of that. It lets you gather much more experimental evidence about what might be true. A good example where you really need the computer is something like the Mandelbrot set.
The Mandelbrot set, Julia sets, and all this stuff which would have been impossible to see without a lot of computation and plotting. Are there any ways in which the computer allows you to solve qualitatively different kinds of problems? I can just say my informal opinion, which is that mathematics is extremely good for highly symmetric objects.
In his monthly column Mathematical Games, which he wrote in Scientific American between the s and the s, he introduced many brainteasers as well as giving old classics new twists. His answer threw me.
Yet when we continued the discussion I realised that my analogies were wrong. There is a difference between being good at puzzles and appreciating a good puzzle. Gardner wrote dozens of books on puzzles and recreational maths — here are eight puzzles taken from them.
- Can you solve Martin Gardner’s best mathematical puzzles?.
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Ten red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?
Two identical bolts are placed together so that their helical grooves intermesh as shown below.
If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so that it does not rotate and twiddling them in the direction shown, will the heads. A logician vacationing in the South Seas finds himself on an island inhabited by two proverbial tribes of liars and truth-tellers. Members of one tribe always tell the truth, members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village.