Mathematics and the Wonders of Creation by James Nickel B.A., B.Th., B.Miss., M.A. Copyright

Creational Harmony Connections with the reality of Creation. –The Physics of Motion (free fall, projectile, planetary orbits, springs, heat, etc.) –Quadratic Equations. Copyright

Creational Harmony Poetry of theorems. –The internal structure of thinking. –The meter and rhyme of logic. –The elegance and beauty of proofs (Pythagorean Theorem, the infinitude of primes, the Fundamental Theorem of Arithmetic, Algebra, and the Calculus, etc.). Copyright

Creational Harmony Unity in Diversity (from geometry to infinite series to probability). e (from interest compounded continually to stunning interconnections in advanced mathematics). (from quantum mechanics to alternating current electricity to the beauties of fractal geometry). Copyright

Stunning Wonder! Copyright Drum roll ………………………………..

Creational Harmony The person of Christ is the source of: –Rationality. –The interconnected wonder of Creation. In Him, all things interconnect (the wholeness of harmony)! Copyright

One Example of Harmony The Golden ratio captures the essence and the spirit of creational harmony. height base Golden Ratio = base/height = Copyright

Golden Ratio Sometimes this ratio is referred to as the ratio of the extreme to the mean. where is the Greek letter phi. Copyright

Mean/Extreme Ratio a b a + b Copyright

Mean/Extreme Ratio Copyright

Mean/Extreme Ratio Copyright

Mean/Extreme Ratio Apply the Quadratic formula Copyright

Amazing Connection 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … What is the pattern? Copyright

The Pattern Copyright , 1, 2, 3, 5, 8, 13, 21, … 1+1=2 1+2=3 2+3=5 3+5=8 5+8= =21

Fibonacci Sequence Named after the Italian mathematician Leonardo Fibonacci ( ). He introduced the work of al Khowarizmi and the Hindu-Arabic positional/decimal system to Christian Europe. Copyright

Fibonacci Sequence He discovered this sequence by studying the population of rabbits and the genealogy of bees. More creation connections: seeds of a daisy head, pine cone and pineapple scales, seeds of a sunflower. Copyright

Question 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … Let F n be the n th term of the sequence. What happens to the ratio F n+1 /F n as n gets larger and larger? Copyright

Answer nF n+1 /F n n 11/1 = 17 21/ /1 = 28 34/ /2 = / / / /5 = / /8 = / Copyright

Limits Copyright

Johannes Kepler ( ) Geometry has two great treasures: one is the theorem of Pythagoras; the other the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. Copyright

Keplers Confession Kepler also stated that when doing mathematics, he was thinking Gods thoughts after Him. Copyright

The Golden Rectangle Begin with a SquareDivide the Square into two equal partsDraw the radius of a circleExtend the base line Draw a portion of a circleComplete the Rectangle, which is Golden By the Pythagorean Theorem: = = 5 The length of the red line is 5 The yellow rectangle is also a Golden Rectangle! 2 Copyright

Why? Copyright Conjugate

Why? Copyright

End with the perfection and wondrous beauty of a Logarithmic Spiral! Start with a Golden Rectangle Copyright

Point O is the center of the Spiral The Center Point of the Logarithmic Spiral A B C D O Draw Diagonals AB and CD Amazing! M N Copyright

Marvelous Unity in Diversity O J K The Logarithmic Spiral is also called an Equiangular Spiral for this reason. Copyright

Fractal Geometry Logarithmic Spiral! Copyright

Chambered Nautilus Logarithmic Spiral in Gods creation. Note how mathematics conforms exactly with the handiwork of God. Copyright

Conclusion Man can think mathematically and the physical creation reflects mathematical patterns because of a common Creator. Copyright

Conclusion Mathematics is an unique tool of wonder. Copyright

Conclusion Studying mathematics in a Biblical way will lead us to better worship and adore our Faithful God! Copyright