, 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

of an enzyme, are incredibly important in biological science, as life cannot exist

without sustained biochemical reactions. So, there is clearly evidence that

Calculus plays a role in the understanding of biology as well. When speaking of

metabolism, the rate quotient (RQ) is equal to the amount of carbon dioxide

released divided by the amount of oxygen consumed. When the lean body mass of

an animal is doubled, the metabolic rate increases by an additional 75%.

Proportionately, though, it goes down.

It is at this point that I would like to exercise some freedom and stray

slightly from the original purpose of the paper. As a first-year student, I am

fortunate in that I am placed in an elite group of three freshmen who are given free

reign in terms of choosing whatever biology courses they want. I am currently

taking two third-year classes and, though my math skills are -to say the least- a bit

discouraging, I had an epiphany one day during one of my independent studies in

maximizing human muscle cell function (by way of increasing efficiency). I, in a

flash of biological/mathematical genius (or maybe just dumb luck ), created a

totally new mathematical formula which determines the maximum amount of

tensile strength (the amount of physical tension that can be placed on an elastic or

semi-elastic object) the skeletal muscle system of the average human being can

withstand. You see, a single muscle fiber is capable of supporting the tension of a

weight equal to one thousand times its own mass before it ruptures. By looking at

cross sectional analyses of human muscle tissue, I was able to determine that there

are, on average, approximately six billion skeletal muscle fibers in the untrained

human body. Therefore, I came to the conclusion that:

AVERAGE HUMAN MUSCULAR CAPACITY =

( Muscle fiber mass ) * 10^3 * ( [~] 6 billion )

I am not absolutely sure what significance this may ultimately hold,

but I can make the assumptions that this formula could be useful when predicting

the durability of pilots of high-speed aircraft such as space shuttles and X-planes.

Also, with advent of genetic engineering, my formula can be the basis for the

creation of more powerful military troops. I have designated each troop to be what

I call an M.D.S., which stands for Most Dangerous Soldier. It is interesting to see

how such a simple mathematical formula can be used to further mankind or

destroy it. Though not nearly as significant as E=mc^2, it holds promise in many

applications, be they for good or for evil.

As you can see, mathematics has much more in common with biological

sciences than it is often given credit for. To forsake the role math plays in the

understanding of life is a grave mistake, and to ignore references to mathematical

advancements of the time long past is to deny our children the opportunity to live

better lives than we do. No one aspect of mathematics or science is more or less

important. It should be viewed in a synergistic fashion. The final result is greater

than the sum of its individual parts.

1. Lawlor, Robert- ?Sacred Geometry?, Thames and Hudson Ldt, 1982.

2. Campbell, Neil A.- ?Biology? (5th edition), Benjamin/Cummings, 1999.

3. Foner, Eric, and Garraty- ?The American Heritage Dictionary?, 1996.

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