images

Numbers in Nature

Theme: Created patterns show God’s fingerprint.

Bible Verse: Where were you when I laid the foundations of the earth? Tell Me, if you have understanding. (Job 38:4)

Materials Needed:

• Flowers

• Other available items mentioned in the lesson

• Pinecones and pine needles

Bible Lesson

Job suffered greatly at the hand of Satan. He lost his children, his health, and his possessions. Most of the book of Job describes the unsuccessful efforts of his friends to comfort him. But in chapter 38, God speaks to Job from a whirlwind, asking a series of profound questions. Job is made to realize that God’s ways are sometimes “past finding out.” In his wisdom, God allows circumstances to happen that we cannot understand from this side of heaven.

In our Bible verse, God asks Job if he was present at the creation. Of course, the answer is no—for Job and for all of mankind. This answer implies that we should not attempt to second-guess exactly how God accomplished creation. In fact, this supernatural event is completely beyond our grasp. The laying of the earth’s foundation describes God’s careful planning of the earth. The next verse describes the marking off of the earth’s dimensions. In other words, mathematical precision was part of the creation details. And still today, arithmetic patterns are found throughout nature.

Job did not have all the answers of life, but he knew that God cared for him even more than the physical creation. Job’s testimony of trust in God, recorded in Job 1:21, should also be ours. It includes the words, “The LORD gave and the LORD has taken away; blessed be the name of the LORD.”

Science Activity

This activity begins with an arithmetic puzzle. On a sheet of paper, blackboard, or screen, write the following numbers and blanks:

1, 1, 2, 3, ______, ______

Ask volunteers to guess the next two missing numbers. Some will correctly guess 5 and 8, each found by adding the two previous numbers in the list, 2 + 3 = 5 and 3 + 5 = 8. This number sequence continues indefinitely. It is called the Fibonacci sequence of numbers, named for the mathematician Leonardo Fibonacci (pronounced fee´-ba-na-chee) of Pisa who lived eight centuries ago.

Now explain that these particular numbers are very common in nature. They frequently occur in the studies of plants and animals. For example, flower petals often come in clusters of 5 or 8. Flower species with 4, 6, or 7 petals can be found, but they occur less often. Pass several objects around the audience or show pictures to a larger group and have them look for Fibonacci numbers. Here are several examples:

Pine needle clusters almost always grow in clusters of two, three, or five needles.

A typical cloverleaf has three petals. Four-leaf clovers exist, but they are mutations or mistakes and are infrequent.

A sand dollar from the sea displays a star pattern with five points on its surface. Most starfish also have five arms.

An apple cut in half will display a five-pointed star in its center.

When counted, the petals of most flower blossoms number five, eight, or higher.

If pinecones are available, the number of distinct spirals around the outside can be counted. The number is very likely 5, 8, or 13. The surface of a pineapple gives similar results. Why does this Fibonacci number pattern appear in nature more often than not? There is no convincing evolutionary explanation. Instead, we see a pattern that the Lord chose to imprint on his works. Creation is not random or accidental but instead shows intelligent design. Challenge the audience to be on the lookout for Fibonacci numbers in nature.

images

Fibonacci numbers are illustrated by three-leaf clovers, flower petals, sand dollars, pine needles, and pinecones.

Science Explanation

Leonardo Fibonacci (1175–1230) is also known as Leonardo of Pisa. During medieval times he made many mathematical discoveries. He is best known for the number sequence that bears his name. After the first two numbers, future entries are generated by the formula

Sn = Sn–1 + Sn–2   n ≥ 3

That is, the next number is the sum of the two preceding numbers. Fibonacci’s initial application of these numbers was to explain the birth pattern of generations of rabbits. This is discussed in many math texts.

The Fibonacci numbers rapidly become large: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, and so on. It is more of a challenge to locate the larger numbers in nature, but they do appear. The study of geometric and numerical patterns in plants is called phyllotaxis. The following list gives many Fibonacci examples from plants and trees.
Aster 21 petals
Buttercup 5 petals
Chicory 21 petals
Daisy Spirals in core of blossom number 21 and 34; petals typically number 34, 55, or 89
Delphinium 8 petals
Eastern white pine Clusters of 5 needles
Enchanter’s nightshade 2 petals
Iris 3 petals
Ivy 3 leaves
Larch conifer Cone has 5 spirals in one direction, 8 in another
Lily 3 petals
Lodgepole pine Clusters of 2 needles
Marigold 13 petals
Michaelmas daisy 89 petals
Norway spruce Cone has 3 spirals in one direction, 5 in another
Oxalis 3 petals
Periwinkle 5 petals
Pineapple Diamond-shaped surface spirals number 8 and 13 in two directions
Plantain 34 petals
Ponderosa pine Clusters of 3 needles
Primrose 5 petals
Pyrethrum 34 petals
Red pine Clusters of 2 needles
Sunflower Spirals of seeds in the flower, depending on the species, number 21 and 34, 34 and 55, 55 and 89, or 89 and 144.
Trillium 3 petals
Virginia creeper 5 leaves

There are also exceptions to Fibonacci numbers in nature, including these:
African violet 4 petals
Clematis 6 petals
Flowering dogwood 4 petals
Honeycomb 6-sided hexagons
Lilac 4 petals
Magnolia blossom 6 petals
Snowflake 6 points

The Fibonacci sequence has many additional interesting properties. For example, the ratio of any two adjacent, larger Fibonacci numbers approaches the golden mean, or 1.618. The fraction 1597⁄987 is close to this number, which is sometimes also called the divine proportion. Rectangular objects with a length-to-width ratio of about 1 to 1.6 are especially pleasing to the eye. The Greek Pantheon was built with its length and width based on this ratio. Many breakfast cereal boxes are also designed with these dimensions in mind to attract our attention. It is also no accident that the piano has an eight-note octave with five black keys and eight white keys.

Fibonacci numbers are embedded everywhere in the fabric of art and science. Mathematics is the language of creation, and these numbers are one example. Today there is an international association dedicated to the mathematical study of Fibonacci numbers. Their journal is called the Fibonacci Quarterly.