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Math As It Relates To Biology Essay, Research Paper

Mathematics as it relates to Biology

Mathematics and many of its aspects are a major part of everyday life. We

spend the majority of our school years studying and learning the concepts of it.

Many times, the question of ?Why do we need to know these things?? has been

asked of a teacher by his or her students. The following will explain the history

and purpose of mathematics in the role of a biologist.

There are various fields that are found within the subject of biology, so

different kinds of mathematics are often utilized that are best suited for special

applications that are required in said areas of work/study. There is, for example, a

sub-field known as bioeconomics. This area focuses on such things as agriculture

and crop yields (among other things). Believe it or not, this science requires a

great deal of Geometry. Geometry is an ancient Greek term meaning ?measure of

the earth?. Even in ancient times, farmers along the Nile river needed Geometry.

You see, in ancient Egypt, the Nile would flood its banks each year, flooding the

land and destroying the farm areas. When the waters receded, the boundaries had

to be redefined so that the farmers could use the mineral-rich silt in order to

maximize crop production

Another interesting aspect of the relationship between mathematics and

biology is what has come to be called the ?Golden Mean.? It was formulated by

Johannes Kepler and it is dryly defined as the division of a line into mean and

extreme ratios. In nature, this becomes highly obvious to the observer. The Golden

Mean is believed to be found wherever and whenever there is and intensification

of function or a particular beauty and harmony of form. Exponents are shown in

the equation spirals based on the roots of 2, 3, and 5. The Golden Mean spiral is

found in nature in the beautiful Nautilus shell. The Nautilus is an animal related to

the octopus. The shape of its shell was discovered by marine biologists to be

responsible for allowing the Nautilus to live so deep in the ocean, as it allows for

adaptation to pressures that occur in very deep water. So, you see, the Golden

Mean spiral is what allows for the existence of one of the most odd creatures of

the marine world. The spiral is also found to be overlapping in the fetus of man

and animals, and ?as you will see- is present in the biological growth patterns of

many plants. This is of great interest to botanists, biologists who specialize in the

study of plants.

For example, the distribution of seeds in a sunflower is governed by the

Golden Mean spiral. The sunflower has 55 clockwise spirals overlaid into either

34 or 89 counterclockwise spirals.

Additionally, the name Fibonacci often appears to describe natural

occurrences. The Fibonacci Series governs the laws involved with physics, but

that is not my point of focus. I would rather have you be drawn towards animal

populations, as the Fibonacci Series portrays the breeding patterns of rabbits, and

the ratio of males to females in the hives of honey bees, wasps, termites, and ants

(basically, any insect that lives in a colony). Such things are interesting to a

population biologist, and it could also be very important to entomologists, which

are biologists who specialize in the study of insects. A botanist would choose to

examine the Fibonacci Series because of the distribution of leaves around a central

stem. All the members of fractions lie between ? and 1/3, creating a situation

where leaves are separated from one another by at least one third of the stem?s

circumference, therefore ensuring a maximum amount of available light and air for

the leaf which is below the preceding one. The Golden Section can be found in all

flowers having five petals or multiples of five, the daisy will always have a

number of petals from the Fibonacci Series. The rose family is one of those based

on five, as are all the flowers of the edible fruit-bearing plants. Walnuts, for

example, grow in clusters of five and six are truly rare (and probably due to

mutation). The plants displaying a six-fold structure such as the tulip, lily, and the

poppy are poisonous or only medicinal for man. The mathematical order found in

nature seems quite astounding, and can often make one wonder if all of this

beauty, order, and structure really is the result of some natural mistake, rather than

a higher power who knows math is rather effective for sorting out the universe, but

I digress.

An amazing amount of math is necessary to be a physiologist. A

physiologist is a type of biologist who studies structure and function. Their

applications of math to their work is amplified when compared to a number of

other kinds of biologists. One of these applications is in the study of respiration

and gas exchange. An example of this can easily be seen with the difference in the

rate of diffusion of oxygen in air and water. 7 ml of O2 can dissolve in one liter of

water, while 209 ml of O2 can dissolve in air. The rate of diffusion in water is

inversely proportional to the square root of molecular weight. All of this is

assumed to be at one atmosphere, which is what the air pressure is at sea level.

Also, for an animal to maintain 44 mm Hg of pressure (up from 40 mm Hg) for

gas exchange, it has to double its rate of respiration. Rates, dealing with reactions

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