Calculus in Genetics Essay

633 Words Aug 22nd, 2010 3 Pages
Introduction

In recent decades the advancements achieved in bioengineering have helped us develop a better understanding of the origins from which humans and other living creatures spur. The discovery of the Deoxyribonucleic acid (DNA) is the key to all bioengineering. The DNA is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms and some viruses. The main role of DNA molecules is the long-term storage of information. An allele is one of two or more forms of the DNA sequence of a particular gene. Each gene can have different alleles. Sometimes different alleles can result in different traits. Occasionally different DNA sequences of alleles will have the same
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To prepare we will create a glossary of our vectors and their magnitudes written in the proper mathematical notation. First we list the components of each vector: a ⃑=√(.29) i ⃑+√(.00) j ⃑+√(.03) k ⃑+√(.68) h ⃑ b ⃑=√(.10) i ⃑+√(.09) j ⃑+√(.12) k ⃑+√(.69) h ⃑ c ⃑=√(.21) i ⃑+√(.07) j ⃑+√(.06) k ⃑+√(.66) h ⃑ d ⃑=√(.22) i ⃑+√(.00) j ⃑+√(.21) k ⃑+√(.57) h ⃑
Second we find the magnitude of each vector: ‖a ⃑ ‖=√(〖√(.29)〗^2+〖√(.00)〗^2+〖√(.03)〗^2+〖√(.68)〗^2 )=1 ‖b ⃑ ‖=√(〖√(.10)〗^2+〖√(.09)〗^2+〖√(.12)〗^2+〖√(.69)〗^2 )=1 ‖c ⃑ ‖=√(〖√(.21)〗^2+〖√(.07)〗^2+〖√(.06)〗^2+〖√(.66)〗^2 )=1 ‖d ⃑ ‖=√(〖√(.22)〗^2+〖√(.00)〗^2+〖√(.21)〗^2+〖√(.57)〗^2 )=1

Using the definition, is the English population closer genetically to the Bantus or the Koreans? Explain.

First we find the angle between the Bantus and the English population by plugging in the values of their components and magnitudes into the dot product equation for finding an angle between two vectors. Then we solve for ”θ.” The angle is:

θ= cos^(-1)⁡((b ⃑∙c ⃑)/‖b ⃑ ‖‖c ⃑ ‖ )=cos^(-1)⁡((√(.1) √(.21)+√(.09) √(.07)+√(.12) √(.06)+√(.69) √(.66))/(1∙1))≈10.272° We use the same process to determine the angle between the Korean and the English population. The angle is:

θ= cos^(-1)⁡〖((d ⃑∙c ⃑)/(‖d ⃑ ‖∙‖c ⃑ ‖ ))=〗 cos^(-1)⁡((√(.22) √(.21)+√(.00) √(.07)+√(.21) √(.06)+√(.57) √(.66))/(1∙1))≈19.857°

When we compare the obtained values for both angles

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