*The following are examples that demonstrate the fun and challenge of identifying the mathematical rules underlying flowers, plants, trees and garden design. Parks are the perfect place to examine the variety of nature's exquisite patterns. *

# Math Trail Examples in Gardens

### New York Botanical Garden

Describe what is meant by self-similarity as evidenced in ferns.

Explain how this relates to the branching veins in deciduous trees.

Name the types of symmetry and patterns you observe in the water lilies and lotuses of the Courtyard Pools.

### Brooklyn Botanic Garden

Cherry Lane West is a quad. Using your stride length, approximate the perimeter of the quad and calculate the length of its diagonal.

Measure the distance between 2 trees in the quad. Is this measurement a line or a line segment? Why?

What type of symmetry is exhibited by the cherry blossom?

### Arizona-Sonora Desert Garden

Which cacti exhibit Fibonacci numbers and which exhibit Lucas numbers?

Which cacti have 5 ribs and how do their rib depths compare?

Which cacti have circular cross sections?

Key to retaining water is the ratio of surface area to volume in a cactus. Compare these ratios in several examples..