Infinite flavor in a finite fruit pastry space!

Further reading: http://www.ams.org/publicoutreach/feature-column/fcarc-circle-limit

Skip to content
# Archimedes Lab Project

## Posts

### Coxeter Disc

### Infinite Pythagorean Triplets

### Golden Ratio (And Its Inverse) In Yin Yang

### A curious right triangle

### Humor: Apple Pi

### The Arithmetic-Geometric Mean Inequality

### When a plane intersects a dodecahedron

### Target 10

### Pascal’s Theorem

### Math Humor

Inspiring and Creative Resources & Tutorials for Science-Curious People

Infinite flavor in a finite fruit pastry space!

Further reading: http://www.ams.org/publicoutreach/feature-column/fcarc-circle-limit

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*+

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…

Mathematics is sometimes weird… Read more: The hole truth of topology.