, 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
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.