Like standard jigsaw puzzles, this puzzle has only one solution, but instead of every piece being a different shape and approximately the same size, every piece is the same shape and 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, for example on pine cones or sunflowers. The puzzle has 8 spirals in one direction, and 13 in the other.

24 days of Books (23)

There are 2 days to Christmas and I thought I would do something a little bit different. So, everyday till Christmas I will post a book recommendation. It will be a math or math related book of course ^_^ Enjoy

The Golden Ratio Coloring Book by Rafael Araujo

Rafael Araujo is a Venezuelan architect and illustrator living in Caracas. For over 40 years he’s been drawing the most beautiful illustrations of nature, entirely by hand. At an old drafting table he adeptly renders the mathematical brilliance of nature with just a pencil, compass, ruler and protractor.

Araujo’s illustrations revolve around intelligent patterns of growth that are ruled by the Golden Ratio. This special number, commonly annotated with the Greek letter Phi (ϕ) can be seen in all sorts of natural spirals, sequences, and proportions. “Phyllotaxis” is the name given for the tendency of organic things to grow in spiral patterns and this number pattern reoccurs so often in nature that some researchers have deemed it a universal law for the perfection of structures, forms, and proportions. From sea shells, leaves, crystals, and even butterfly wings, Phi can be traced throughout our environment, time and time again.

The artist applies the Golden Ratio to his drawings and leaves the construction lines in the final images, which gives an incredible beautiful effect to the drawings. 

Signs I need a life...and sleep

1. I take our group’s metaphor for clinical reasoning (a growing, fruiting tree) to the point of ranting about phyllotaxy (how leaves arrange themselves optimally on branches)

2. I find myself unconsciously attracted to radiograph close-ups of the glenohumeral joint

3. Everything is funny….the word bleb from pathology lecture…the word babygram from medical imaging….everything


Haworthia truncata is in the family Xanthorrhoeaceae. Like many other species of Haworthia, it is native to the Little Karoo region of South Africa. The specific epithet, “truncata”, refers to the shape of the tips of the leaves, which give the leaves a truncated appearance. This species is stemless with the leaves being born from an underground meristem and arranged in two parallel rows, known botanically as distichous phyllotaxy. Haworthia truncata is popularly cultivated as a house plant, and is quite hardy in cultivation. This is due to the fact that this plant naturally occurs in dry, arid deserts with extreme temperature fluctuations, making this plant amenable to indoor growing conditions.