1. Mathematics and the Wonders of Creation by James Nickel B.A., B.Th., B.Miss., M.A. Copyright 2008-2009 www.biblicalchristianworldview.net

2. Creational Harmony Connections with the reality of Creation. –The Physics of Motion (free fall, projectile, planetary orbits, springs, heat, etc.) –Quadratic Equations. Copyright 2008-2009 www.biblicalchristianworldview.net

3. 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 2008-2009 www.biblicalchristianworldview.net

4. Creational Harmony Unity in Diversity. 3.14 (from geometry to infinite series to probability). e 2.718 (from interest compounded continually to stunning interconnections in advanced mathematics). (from quantum mechanics to alternating current electricity to the beauties of fractal geometry). Copyright 2008-2009 www.biblicalchristianworldview.net

6. Stunning Wonder! Copyright 2008-2009 www.biblicalchristianworldview.net Drum roll ………………………………..

7. 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 2008-2009 www.biblicalchristianworldview.net

8. One Example of Harmony The Golden ratio captures the essence and the spirit of creational harmony. height base Golden Ratio = base/height = Copyright 2008-2009 www.biblicalchristianworldview.net

9. Golden Ratio Sometimes this ratio is referred to as the ratio of the extreme to the mean. where is the Greek letter phi. Copyright 2008-2009 www.biblicalchristianworldview.net

10. Mean/Extreme Ratio a b a + b Copyright 2008-2009 www.biblicalchristianworldview.net

11. Mean/Extreme Ratio Copyright 2008-2009 www.biblicalchristianworldview.net

12. Mean/Extreme Ratio Copyright 2008-2009 www.biblicalchristianworldview.net

13. Mean/Extreme Ratio Apply the Quadratic formula Copyright 2008-2009 www.biblicalchristianworldview.net

14. Amazing Connection 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … What is the pattern? Copyright 2008-2009 www.biblicalchristianworldview.net

15. The Pattern Copyright 2008-2009 www.biblicalchristianworldview.net 1, 1, 2, 3, 5, 8, 13, 21, … 1+1=2 1+2=3 2+3=5 3+5=8 5+8=13 8+13=21

16. Fibonacci Sequence Named after the Italian mathematician Leonardo Fibonacci (1170-1230). He introduced the work of al Khowarizmi and the Hindu-Arabic positional/decimal system to Christian Europe. Copyright 2008-2009 www.biblicalchristianworldview.net

17. 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 2008-2009 www.biblicalchristianworldview.net

18. 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 2008-2009 www.biblicalchristianworldview.net

19. Answer nF n+1 /F n n 11/1 = 17 21/13 1.615 22/1 = 28 34/21 1.619 33/2 = 1.59 55/34 1.618 4 5/3 1.67 10 89/55 1.618 58/5 = 1.611 144/89 1.618 613/8 = 1.62512 233/144 1.618 Copyright 2008-2009 www.biblicalchristianworldview.net

20. Limits Copyright 2008-2009 www.biblicalchristianworldview.net

21. Johannes Kepler (1571-1630) 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 2008-2009 www.biblicalchristianworldview.net

22. Keplers Confession Kepler also stated that when doing mathematics, he was thinking Gods thoughts after Him. Copyright 2008-2009 www.biblicalchristianworldview.net

23. 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 2 11 2 By the Pythagorean Theorem: 1 2 + 2 2 = 1 + 4 = 5 The length of the red line is 5 The yellow rectangle is also a Golden Rectangle! 2 Copyright 2008-2009 www.biblicalchristianworldview.net

24. Why? Copyright 2008-2009 www.biblicalchristianworldview.net Conjugate

25. Why? Copyright 2008-2009 www.biblicalchristianworldview.net

26. 1 2 3 4 5 6 End with the perfection and wondrous beauty of a Logarithmic Spiral! Start with a Golden Rectangle Copyright 2008-2009 www.biblicalchristianworldview.net

27. 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 2008-2009 www.biblicalchristianworldview.net

28. Marvelous Unity in Diversity O J K The Logarithmic Spiral is also called an Equiangular Spiral for this reason. Copyright 2008-2009 www.biblicalchristianworldview.net

29. Fractal Geometry Logarithmic Spiral! Copyright 2008-2009 www.biblicalchristianworldview.net

30. Chambered Nautilus Logarithmic Spiral in Gods creation. Note how mathematics conforms exactly with the handiwork of God. Copyright 2008-2009 www.biblicalchristianworldview.net

31. Conclusion Man can think mathematically and the physical creation reflects mathematical patterns because of a common Creator. Copyright 2008-2009 www.biblicalchristianworldview.net

32. Conclusion Mathematics is an unique tool of wonder. Copyright 2008-2009 www.biblicalchristianworldview.net

33. Conclusion Studying mathematics in a Biblical way will lead us to better worship and adore our Faithful God! Copyright 2008-2009 www.biblicalchristianworldview.net