this magic internet

If you visit Arizona you can hardly fail to miss the impressive saguaro cacti that march up the foothills of the mountains near Tucson. So it's not totally surprising to find that a bunch of Arizona mathematicians have turned their minds to the beautiful patterns in cacti. In particular, how do the striking patterns of ribs arise? Patrick Shipman and Alan Newell, at the University of Arizona in Tucson, have provided an important part of the answer. It all depends on elasticity. A Saguaro Cactus outside Cave Creek Arizona Since ancient times, people have noticed strange numerical patterns in plants. Marigolds have 13 petals, asters have 21, daisies have 34, 55, or 89, and sunflowers have 55, 89, or 144. These numbers have been familiar to mathematicians since 1202, when the Italian mathematician Leonardo of Pisa posed a problem about rabbits. His somewhat unrealistic rabbit population increased according to a fascinating sequence of numbers: 1 1 2 3 5 8 13 21 34 55 89 144 23

Over the years many styles to classify Bonsai trees have been advanced, closely resembling circumstances in nature. These styles are open to personal interpretation and creativity, meaning that trees do not necessarily need to conform to any form. Still, the styles are important to gain a basic understanding of shapes and should serve as guidelines to successfully train miniature trees. Broom style Bonsai Hokidachi The broom style is suited for deciduous trees with extensive, fine branching. The trunk is straight and upright and does not continue to the top of the tree; it branches out in all directions at about 1/3 the height of the tree. The branches and leaves form a ball-shaped crown which is also a stunning sight during winter months. Formal upright Bonsai style Chokkan The formal upright style is a very common form of Bonsai. This style often occurs in nature, especially when the tree is exposed to lots of light and does not