Pannal, Ticson, B , BSCRIM3
1.Fibonacci Sequence: 5.Spirals
Examples: arrangement of leaves around a stem Examples; Spiral shell & seed
2.Golden Ratio 6. Tessellation
Examples :shape of galaxies Examples: Fish scale & honeycomb
3.Fractals
Examples Branching pattern of trees and snow flakes
4 Symmetry
Examples : Butterfly & Starfish
1 The Fibonacci Sequence: Nature’s Code The Fibonacci sequence is a series of numbers in which each number is
the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8, 13...). This sequence appears in various patterns in
nature, including:
-Flower Petals: Many flowers have a number of petals that corresponds to a Fibonacci number (e.g., 3, 5, 8, 13). [2]
-Leaf Arrangement: The arrangement of leaves on a stem often follows a Fibonacci spiral, ensuring that each leaf
receives optimal sunlight. [2
-Branching Patterns: The branching patterns of trees and other plants can also be described
2. The golden ratio, approximately 1.618, is a fascinating mathematical concept that
appears in various natural patterns, suggesting its fundamental role in growth and
development. It’s closely related to the Fibonacci sequence, where each number is the sum
of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8, 13...). examples of the golden ratio
- Spiral Galaxies: Spiral galaxies, including our own Milky Way, exhibit a logarithmic spiral
pattern with a growth factor close to the golden ratio.
3.Fractals are intricate geometric shapes that exhibit self-similarity, meaning they have the
same pattern at different scales or magnifications. They are found abundantly in nature,
from the branching patterns of trees to the irregular shapes of coastlines.
- Coastlines: The coastline of any landmass is an excellent example of a fractal. As you zoom
in or out, the irregularities and intricate details persist, regardless of the scale.
- Snowflakes: The intricate pattern of a snowflake is a mesmerizing example of a fractal. As
snow crystals form, the intricate branching patterns emerge due to the interaction of
temperature and humidity. Each branch exhibits the same intricate shape as the overall
snowflake, creating a beautiful and unique structure.
4.Symmetry is a fundamental concept in mathematics, and it is ubiquitous in the natural
world. It refers to the balanced arrangement of parts or shapes that are mirror images or
rotationally identical. The symmetrical patterns we observe in nature evoke a sense of
harmony and visual appeal.
-Butterflies: The intricate symmetry of butterfly wings is a captivating sight. Each wing
displays perfect mirror-image patterns, ensuring balance and aerodynamic efficiency.
5.Spirals are another common pattern in nature, often associated with growth and
development. They can be found in various forms, including:
- Nautilus Shells: The shell of a nautilus is a classic example of a spiral pattern. As the
nautilus grows, it adds chambers to its shell, following a logarithmic spiral that maintains the
shell’s proportional
- Sunflowers: The seeds of sunflowers are arranged in a spiral pattern, following the
Fibonacci sequence. This arrangement maximizes the number of seeds that can be packed
into the flower head.
6.Tessellations: Nature’s Tiling Patterns
Tessellations are patterns made by repeatedly tiling the same or similar shapes. They can be
found in various natural structures:
- Honeycombs: Honeycombs are a classic example of a tessellation. Bees instinctively
construct hexagonal compartments, which are arranged in striking symmetry. This structure
is believed to be the most efficient for storing honey with the least amount of wax.
- Animal Skins: The scales of snakes and pangolins are arranged in tessellation patterns.
These patterns provide camouflage and protection for the animals.
