There are only five integer-sided triangles whose area is numerically equal to its perimeter:
(5, 12, 13), (6, 8, 10), (6, 25, 29), (7, 15, 20), and (9, 10, 17)
As you can see from the picture, only 2 of them are right triangles.
Elementary 4-manifold topology
Cut any of the loops of strings below and the whole chain comes apart.
You will find many of these kinds of puzzles in my book “Impossible Folding Puzzles and Other Mathematical Paradoxes” .
Infinite Pythagorean Triplets
Consider the following simple progression of whole and fractional numbers (with odd denominators):
1 1/3, 2 2/5, 3 3/7, 4 4/9, 5 5/11, 6 6/13, 7 7/15, 8 8/17, 9 9/19, …
Any term of this progression can produce a Pythagorean triplet, for instance:
4 4/9 = 40/9; the numbers 40 and 9 are the sides of a right triangle, and the hypotenuse is one greater than the largest side (40 + 1 = 41).
Golden Ratio (And Its Inverse) In Yin Yang
The philosophy of the Yin Yang is depicted by the the “taichi symbol” (taijitu). In fact, Yin Yang is a concept of dualism, describing how seemingly opposite or contrary forces may actually be complementary,
Curiously enough, in the taichi symbol are hidden the golden ratio and its reverse. As shown in the picture. Continue reading “Golden Ratio (And Its Inverse) In Yin Yang”
Target 10
Here is a little puzzle of our creation you can make with your kids or in class…
“Stubborn” Number 33
It is conjectured that n is a sum of 3 cubes if n is a number that is not congruent to 4 or 5 mod 9. The number 33 enters this category, but for 64 years no solutions emerged — that is, whether the equation 33 = x³ + y³ + z³ has an integer solution. Continue reading ““Stubborn” Number 33″
Sangaku: Semicircle inscribed in a right triangle
Find the radius r of the semicircle inscribed in the right triangle below:
show solution
Smallest Prime Number Magic Square
American mathematician Harry L. Nelson won the challenge to produce a 3 × 3 magic square containing the smallest consecutive primes:
Fibonacci Spiral Jigsaw Puzzle
Each piece of this puzzle is similar (the same shape at a different size). The placement of the pieces is based on the golden angle (≈137.5º), and results in a pattern frequently found in nature (phyllotaxis), for instance on sunflowers. The puzzle features 8 spirals in one direction, and 13 in the other. You can build your own Fibonacci spiral puzzle by following John Edmark’s tutorial.
Illusive Number
If you can see the 8 in the middle of the 8 of diamonds you are a visual thinker rather than a verbal thinker.
