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

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

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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

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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

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

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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

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

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

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Mean/Extreme Ratio a b a + b Copyright

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Mean/Extreme Ratio Copyright

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Mean/Extreme Ratio Copyright

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Mean/Extreme Ratio Apply the Quadratic formula Copyright

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

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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

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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

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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

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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

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

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Limits Copyright

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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

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

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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

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Why? Copyright Conjugate

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Why? Copyright

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

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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

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

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Fractal Geometry Logarithmic Spiral! Copyright

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

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

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Conclusion Mathematics is an unique tool of wonder. Copyright

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

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