Patterns and Functions in Mathematics

Which of the following is not considered a pattern in nature?

• Symmetry

• Bubbles

• Tessellations

• Fractions

Answer explanation

Bubbles are not a consistent pattern in nature; they are transient and random. In contrast, symmetry, tessellations, and fractions represent structured patterns found in various natural forms.

The Fibonacci Sequence begins with which of the following pairs of numbers?

• 0, 1

• 1, 2

• 1, 3

• 2, 3

Answer explanation

The Fibonacci Sequence starts with the numbers 0 and 1. Each subsequent number is the sum of the two preceding ones, making 0 and 1 the correct initial pair.

Which number is the 6th term in the Fibonacci sequence?

• 5

• 8

• 13

• 21

Answer explanation

The Fibonacci sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, ... The 6th term is 13, as it is the sum of the 4th (3) and 5th (5) terms.

The Golden Ratio is approximately equal to:

• 2.17

• 3.14

• 1.618

• 1.71

Answer explanation

The Golden Ratio, often denoted by the Greek letter phi (φ), is approximately 1.618. This ratio is significant in art, architecture, and nature, making 1.618 the correct choice among the options provided.

Which flower’s petals follow the Fibonacci sequence?

• Lily

• Rose

• Daisy

• Sunflower

Answer explanation

The sunflower's petals often exhibit the Fibonacci sequence, where the number of petals corresponds to Fibonacci numbers like 34 or 55. This pattern is a common occurrence in nature, making the sunflower the correct choice.

The ratio of consecutive Fibonacci numbers approximates:

• 3.14

• 1.618

• 0.618

• 2.71

Answer explanation

The ratio of consecutive Fibonacci numbers approaches the golden ratio, approximately 1.618. This value is significant in mathematics and appears in various natural phenomena.

The Fibonacci sequence appears in all of the following except:

• Tree branches

• Hurricane spirals

• Mountain heights

• Flower petals

Answer explanation

The Fibonacci sequence is commonly found in nature, such as in tree branches, hurricane spirals, and flower petals. However, it does not have a direct correlation with mountain heights, making it the correct answer.

In nature, equiangular spirals are most commonly seen in:

• Galaxies

• Waves

• Tree leaves

• Rainbows

Answer explanation

Equiangular spirals are commonly observed in galaxies, where the arms of the galaxy follow this spiral pattern. This phenomenon is less applicable to waves, tree leaves, or rainbows.

What property distinguishes Fibonacci spirals from other types of spirals?

• Constant radius

• Constant angle between turns

• Changing curvature

• Decreasing radius

Answer explanation

Fibonacci spirals are characterized by a constant angle between turns, which differentiates them from other spirals that may have varying angles or radii. This property creates a unique growth pattern found in nature.

Which term in the Fibonacci sequence is closest to 21?

• F(6)

• F(7)

• F(8)

• F(9)

Answer explanation

In the Fibonacci sequence, F(6) = 8, F(7) = 13, F(8) = 21, and F(9) = 34. The term F(8) is exactly 21, making it the closest term to 21.