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).
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”
The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.
A visual intuitive proof that √ab cannot be larger than (a+b)/2, where a, b ∈ R*+
Continue reading “The Arithmetic-Geometric Mean Inequality”
A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon.
Here is a little puzzle of our creation you can make with your kids or in class…
Continue reading “Target 10”
No matter how you choose to place the red points on the circumference, the three blue points will lie on a straight line (shown in red). This works for any conic (which may be a circle, ellipse, parabola or hyperbola).
Mathematics is sometimes weird… Read more: The hole truth of topology.
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″