The National Student Research Center

E-Journal of Student Research: Multi-Disciplinary

Volume 5, Number 4, June, 1997

The National Student Research Center is dedicated to promoting student research and the use of the scientific method in all subject areas across the curriculum, especially science and math.

For more information contact:

John I. Swang, Ph.D.
Founder/Director
National Student Research Center
2024 Livingston Street
Mandeville, Louisiana 70448
U.S.A.
E-Mail: nsrcmms@communique.net
http://youth.net/nsrc/nsrc.html

Science:

Cylindrical Electro-Chemical Deposition In A Gel
The Amount Of Electrical Resistance In Different Materials
Can Vitamin C be Destroyed by Microwave Heat?
Testing the pH of Water Sources
Does The Temperature Of Water Affect The Growth And Germination Of A Seed?
The Search for the Perfect Wax
An Infinite Number Of Monkeys . . . A Study Of Random Word Generation

Math:

The Relationship of the Volumes of Pyramids and Prisms

Social Studies:

What Do Students Know And Feel About Poverty In The USA?
What Students Know and Feel About Child Abuse

SCIENCE SECTION


TITLE:  Cylindrical Electro-Chemical Deposition In A Gel

STUDENT RESEARCHERS:  Chris Churchill, David Benson Haglund,
                      and Samantha Huang. 
SCHOOL ADDRESS: Belmont High School
                221 Concord Ave.
                Belmont, MA 02178
GRADE: 12
TEACHER: Paul Hickman- namkcihp@aol.com

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

We wanted to find out about how the medium affects the growth 
of a fractal, specifically the growth of a copper aggregate in 
an electro-chemical cell.  By comparing the growth of the 
copper aggregate in gels of different concentrations and in a 
liquid, we hoped to see how the medium affects the fractal 
dimension of the aggregate.  We hypothesized that the viscosity 
of the medium will have a significant effect on the fractal 
dimension of the aggregate.  The denser the medium, the higher 
the fractal dimension.  

II.  METHODOLOGY:

When we initially set out to grow an aggregate in a gel we 
decided to try growing the aggregates in an agar medium.  The 
original medium was a mixture of 0.9 grams of agar and 75 mL of 
a 0.4 M Copper Sulfate solution.  We placed two copper wires in 
the cell and waited until it gelled.  We then connected the 
wires to a power supply and an ammeter and set the power supply 
to 8V.

Almost immediately, there was a bubbling around the cathode.  
The gel then began to crack and separate.  A blue solid began 
to collect around the cathode, but remained in the gel, 
apparently not depositing on the cathode.  A black film 
appeared on the cathode.  A copper colored solid began to 
collect around the anode as well.  As of yet we have come up 
with no reasonable explanation that accounts for all of these 
phenomena.

After a few similarly fated trials we decided to use the 
following procedure in growing our aggregates.  We adopted the 
method of electro-chemical deposition of copper which we used 
in class, with only minor changes.  

1.  Cell Set-up.

Material needed: a power supply, copper wires, a piece of 
rectangular copper, and a cylindrical, transparent container.  

A.  Circuit diagram: 

B.  The container needs to be lined with the piece of 
rectangular copper sheet.  This sheet is to become the anode in 
the cell.  This sheet will then provide a uniform distribution 
of positive charges along the sides of the cylindrical 
container.  A piece of copper wire needs to be bent and fixed 
so that it stands straight in the middle of the container.  
This straight piece of copper is to be the cathode.  In the 
container, we put in media of different concentrations of an 
agar/copper sulfur solution.  This will be explained below. 

2.  Medium.

We used four different kind of medium.  Each of them has a 
different concentration.  Three of the medium we used were 
agars.  They were mixed as described below:

A.  Make 500mL of 0.9 M copper sulfate solution.
B.  Weigh 0.9 g of Agar.  Mix Agar with 75 mL of copper 
sulfate solution over heat.  Stir and heat until all the Agar 
is dissolved.  
C.  Pour out 25 mL of the agar/copper sulfate solution, into 
the first cell.  Label it as Concentration 1 so you can 
remember which one it is.
D.  Pour 50 more milliliters of copper sulfate solution into 
the remaining agar/copper sulfate solution.  Stir over heat 
until the solution looks homogeneous.
E.  Pour out 25mL of the second agar/copper sulfate 
solution, into the second container.  Label as Concentration 2.  
This gel has a smaller concentration than the first gel. 
F.  Pour into the remaining solution 50mL of copper sulfate.  
Stir and heat until the solution looks homogeneous.  
G.  Pour 25mL of this solution into the third cell.  Let all 
the cells settle.  All solutions will gel in about an hour.

3.  Connect the cell with the ammeter and the power supply.  
Turn on the power supply, set the voltage to 4.5 V, and run the 
experiment.  Take data every thirty seconds for current 
(ampere) and diameter of the deposition (mm).  
 
III.  ANALYSIS OF DATA:
 
The data is taken every thirty seconds during the electro-
deposition.  The data includes the diameter of the fractal 
copper deposition, time, and the current.  The data is what we 
needed to make the graph, the diameter and the relative mass.  
The relative mass of the fractal object is gotten by 
multiplying the time and the current, since the mass of the 
object is proportional to the time of growth and to the current 
that is passing through the gel.  The data also showed the 
natural log of both the diameter and the relative mass.  The 
natural log of the diameter is the x-axis of the graph while 
the natural log of the relative mass is the y-axis of the 
graph.  Our data showed that the denser the gel, the slower it 
grows (in terms of distance), and the higher the fractal 
dimension. 

IV.  SUMMARY AND CONCLUSION:

We discovered that our hypothesis was correct.  When a copper 
aggregate is grown in a gel, it deposits in the droplets of 
water that are dispersed through the gel.  These droplets are 
less numerous when there is less agar powder in the gel.  The 
analogy we found most useful to explain this is the forest 
program.  The higher the critical probability, the more 
connected the forest, and therefore, the less empty spaces.  
The copper deposits in these empty spaces.  Due to the 
restriction of movement in the more concentrated gels, the 
Copper ions have less freedom to travel to the forming 
aggregate.  Therefore they will deposit to the closest portion 
of the aggregate that they can reach instead of moving off and 
forming branches.

V.  APPLICATION:

Through our experiments, we have discovered the mechanisms 
behind electrical deposition of copper sulfate through medium 
of different concentrations.  One of our discoveries is that 
the denser the medium, the higher the fractal dimension.  Our 
rationalization for this phenomenon is that, since the copper 
ions have to travel through the medium to the cathode of the 
cell and get attached to the cathode, each branch of copper 
deposit would become a cathode themselves and is full of 
electrons.  This means that each branch has a negative charge.  
Therefore, each branch repels each other.  In a denser medium, 
the force of repulsion between the branches is not enough to 
repel each other apart as far away as they could in a less 
dense medium because of the resistance that the denser medium 
put upon the branches.  Also, in a denser medium, there is not 
as much room for movement as there is in a less dense liquid.  
Therefore, the copper ions can only deposit themselves to the 
closest place instead of being pushed to the ends of the 
branches by the electric field forces.  We have also discovered 
something about the structure of gels.  We believe that gels 
consist of a sponge-like super-structure, with a liquid trapped 
in the empty spaces.



TITLE:  The Amount Of Electrical Resistance In Different 
        Materials

STUDENT RESEARCHER:  Amanda Guillory and Karla Hardberger
SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John I. Swang, Ph.D.

I.  STATEMENT OF PURPOSE AND HYPOTHESIS: 

We would like to do a scientific research on which substances 
conduct electricity.  Our hypothesis states that there will be 
no electrical resistance in the metals that we test.

II.  METHODOLOGY:

First we wrote our statement of purpose, review of literature, 
bibliography, hypothesis, and methodology.  Next we gathered 
our materials:  aluminum, copper, iron, distilled water, salt 
water, plastic, paper, wood, cotton cloth, synthetic cloth, 
rubber, pencil, data collection form, and an ohm meter.  Then 
we tested each of the materials by using the ohm meter to 
measure the amount of electrical resistance each material had.  
Then we recorded our data on the data collection form.  After 
that, we conducted our analysis of data, and wrote our summary 
and conclusion and application.  Finally, we printed our 
research in the journal of the National Student Research Center 
and published it on the Internet.   

III.  ANALYSIS OF DATA:

In our experiment, we found that aluminum, copper, iron, gold, 
white gold, and sterling silver have zero ohms of resistance.  
Salt water has 175 ohms of resistance.  Distilled water, tap 
water, plastic, paper, wood, cotton cloth, synthetic cloth, 
rubber, and paint all have 1000 ohms of resistance.

Materials      |  T1  |  T2  |  T3  |  Avg.|
               | Omhs | Omhs | Omhs | Omhs |
Aluminum       |  0   |  0   |  0   |  0   |
Copper         |  0   |  0   |  0   |  0   |
Iron           |  0   |  0   |  0   |  0   |
Gold           |  0   |  0   |  0   |  0   |
White Gold     |  0   |  0   |  0   |  0   |
Sterling Silver|  0   |  0   |  0   |  0   |
Salt Water     |  175 |  175 |  175 |  175 |
Distilled Water| 1000 | 1000 | 1000 | 1000 |
Tap Water      | 1000 | 1000 | 1000 | 1000 |
Plastic        | 1000 | 1000 | 1000 | 1000 |
Paper          | 1000 | 1000 | 1000 | 1000 |
Wood           | 1000 | 1000 | 1000 | 1000 |
Cotton Cloth   | 1000 | 1000 | 1000 | 1000 |
Synthetic Cloth| 1000 | 1000 | 1000 | 1000 |
Rubber         | 1000 | 1000 | 1000 | 1000 |
Paint          | 1000 | 1000 | 1000 | 1000 |

IV.  SUMMARY AND CONCLUSION:

We found in our experiment, that distilled water, plastic, 
paper, wood, cotton cloth, synthetic cloth, rubber, tap water, 
and paint do not conduct electricity.  There were zero ohms of 
resistance found in aluminum, copper, iron, gold, white gold, 
sterling silver, and salt water.  Therefore we accept our 
hypothesis which stated that there will be no electrical 
resistance in the metals that we tested.

V.  APPLICATION:

We can apply our findings to the world outside the classroom by 
using the materials that had very little, or no resistance as 
conductors of electricity.



TITLE:  Can Vitamin C be Destroyed by Microwave Heat?

STUDENT RESEARCHER:  Christine Louie
SCHOOL:  Westminster School  
         3819 Gallows Road   
         Annandale, Virginia  22041  
GRADE:  7
TEACHER:  Paul Favata

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

Vitamin C is found in almost all plant foods but not in meat.  
Lack of Vitamin C results in scurvy.  Symptoms of scurvy are 
swollen gums, wounds that don't heal, broken blood vessels, and 
a general lack of energy.  The minimum daily requirement of 
Vitamin C to prevent scurvy is 30 mg per day.  The RDA of 
Vitamin C is 60 mg per day.

People often use microwaves to cook or heat up food (pies, 
vegetables, etc.).  I was wondering whether or not microwave 
heat destroyed Vitamin C in fruits, and if so, how much?  My 
hypothesis stated that Vitamin C can be destroyed by microwave 
heat.

II.  METHODOLOGY:

Materials -

7 Red Delicious apples & 4 tomatoes
buret
juicer
Erlenmeyer flask (125 ml)
3 M HCl
0.01 M iodine solution
filter paper
distilled water
pipettes
pipette bulb
4% starch solution

Procedure -

1) Peel and core the apple. Run the apple through the juicer.
2) Filter the apple juice through the filter paper.
3) Pipette 10 ml of the apple juice into the flask.
4) Add 20 ml of distilled water.
5) Add 5 drops of 3 M HCl (the HCl acts as a catalyst; it 
speeds the reaction up).
6) Put in 10 drops of starch solution (indicator).
7) Add the iodine solution with the buret a drop at a time 
until the indicator changes to dark blue.**
8) Read the buret and record the amount of iodine solution used 
in milliliters.
9) Repeat steps 1-9 using apples microwaved for 4 minutes on 
high.
10) Calculate concentration of Vitamin C.
11) Repeat experiment using tomatoes instead of apples.

**Here's how the reaction between the Vitamin C, starch, and 
iodine works.  When starch reacts with iodine, the solution 
turns a dark blue.  However, in the experiment, there is also 
Vitamin C (the fruit juice) in the starch solution.  When the 
iodine is put into the solution, it first oxidizes the Vitamin 
C.  When all of the Vitamin C is oxidized, the iodine then 
reacts with the starch.  The amount of iodine solution use then 
indicates the amount of Vitamin C in the solution.

III.  ANALYSIS OF DATA:

I did the experiment with both apples and tomatoes three times 
before and three times after cooking.  The 7 apples produced 
277 cc of apple juice (40 cc/apple), and the 4 tomatoes 
produced 242 cc of juice (60 cc/tomato).

For the apple experiment, the uncooked apple showed 70mg of 
Vitamin C/1000cc of juice as a result.  Since the average 
measured liquid volume of an uncooked apple is 40 cc, then the 
average apple tested has 2.8 mg of Vitamin C/apple 
(70mg/1000cc=2.8mg/40cc).  The cooked apple showed the same 
results (2.8mg/40cc).  However, the volume of the cooked apple 
juice was only 70 cc (as compared to 277 cc for the uncooked 
apple juice) mostly due to evaporation, but a large amount of 
Vitamin C may have been destroyed (which explains why the 
results were the same).  
  
For the tomatoes, the result for the uncooked tomatoes was 
210mg of Vitamin C/1000cc of juice.  Because the average amount 
of liquid for an uncooked tomato was 60 cc, the average tomato 
tested has 12.6 mg of Vitamin C per tomato 
(210mg/1000cc=12.6mg/60cc).  For the cooked tomatoes, the 
result was 240mg/1000cc.  The amount of liquid for the cooked 
tomatoes was 60 cc (as compared to the total of 242 cc for the 
uncooked tomatoes), mostly due to evaporation.  However, as was 
the case with the apples, a certain amount of Vitamin C may 
have been destroyed.

IV.  SUMMARY AND CONCLUSION:

My hypothesis seems to be supported by my data.  Even though 
microwave cooking heats differently than stoves and ovens, its 
effect on Vitamin C appears to be the same.  Therefore, I 
accept my hypothesis which stated that Vitamin C can be 
destroyed by microwave heat.



TITLE:  Testing the pH of Water Sources.

STUDENT RESEARCHER:  Erin Phillips and Katie Goodwin

SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John I. Swang, Ph.D.

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

We would like to do a scientific research project on testing 
the pH of different sources of water.  We will be testing 
sources of water from around the city.  Our hypothesis states 
that we will find a high acidic level in the water samples we 
will test from our city.

II.  METHODOLOGY:

First, we wrote our statement of purpose and review of the 
literature on acids, bases, alkali, and pH.  Then we developed 
our hypothesis.  Next, we wrote our methodology.  Then we 
gathered our materials.  Next, we took samples of water from 
different sources around the city: our kitchen faucets, bottled 
water, rain, distilled water, Lake Ponchartrain, a pond in the 
Lakes subdivision, ditch water, and the Tchefuncte River.  Then 
we used ph paper to test the pH of the water.  Then we recorded 
our first set of data.  A few days later, we gathered more 
water samples and re-tested them.  Then we recorded our second 
set of data.  Then we wrote our analysis of data, summary and 
conclusion, and application.  Finally, we applied our findings 
to the world outside the classroom and published our project on 
the Internet.

III.  ANALYSIS OF DATA:

All of the samples from natural sources of water were drawn 
from the exact same spot, just on different days.  The average 
pH of the six samples of bottled water was 7.2, very neutral.  
The average pH of the six samples of the distilled water was 5, 
which is very acidic for water.  The average pH of the six 
samples of ditch water was 6.5, which is slightly acidic.  The 
average pH of the six samples of Lake Ponchartrain's water was 
5.5, which is quite acidic for water.  The average pH of the 
six samples of the tap water was 6.2, which is slightly acidic, 
at least for water.  The average pH of the six samples of the 
Tchefuncte River's water was 6.7, which is almost neutral, but 
not quite.

Water Sample      |    Average pH  |
                  |                |
Bottled           |     7.2        |
Distilled         |       5        |
Ditch             |     6.5        |
Lake Ponchartrain |     5.5        |
Pond              |     6.7        |
Tap Water         |     6.2        |
Tchefuncte River  |     6.7        |

IV.  SUMMARY AND CONCLUSION:

In our experiment, we found out almost all of the natural 
sources of water had either an acidic pH level.  This could be 
a very serious problem in the future because acidic water 
affects plant growth and it also affects the quality of the 
food grown around the State of Louisiana.

However, the bottled water, Naya, which came from Canada, had a 
very basic pH level of 7.2.  This may indicate that the State 
of Louisiana has more of a problem dealing with acidic water 
than Canada does.

From the findings in our experiment, we accept our hypothesis 
which states that we think that our city's water level will 
have a problem with water acidity.

V.  APPLICATION:

This information could be quite useful in the future since 
scientists are so concerned with the quality of our earth's 
natural resources, water included.  The scientists could read 
our project on the Internet and consult our findings and try to 
determine the problem with pollution, which causes acid rain, 
and find a way to solve the problem.



Title:  Does The Temperature Of Water Affect The Growth And   
        Germination Of A Seed?

Student Researcher:  Kimberly S. Bellware
School Address:  Hillside Middle School
                 1941 Alamo
                 Kalamazoo, Michigan 49007
Grade:  Seventh
Teacher:  Barbara A. Minar

I.  Statement of Purpose and Hypothesis: 

In my experiment, I wanted to find out if water had an effect 
on the growth and germination of a seed.  I wanted to compare 
seeds soaked and watered with room temperature water and seeds 
soaked and watered with cold water.  My hypothesis stated that 
seeds soaked and watered with room temperature water will grow 
taller. 

II.  Methodology: 

The materials I used were: two clay pots of the same size, 
American Gro brand potting soil, American Seed brand Alaska 
peas, a mini shovel, a measuring cup. two clear plastic cups 
(same size), two and one-half cups of water, measuring spoons, 
and a ruler.  My manipulated variable was the temperature of 
the water used to soak the seeds. My control variables were, 
the type of seed, seed brand, soil brand, depth of seed when 
sowed, amount of water, amount of sunlight, amount of time 
seeds are soaked, size of pots, brand of pots, amount of soil, 
and room environment.  First, I took six American Seed brand 
pea seeds and separate them into two equal groups of three. 
Then I put three into a clear, plastic cup labeled 'C.' I put 
the other three into a clear plastic cup labeled 'W.' Then I 
soaked the three seeds in the cup labeled 'C' with cold water 
for 24 hrs.  I also soaked the three seeds in the cup labeled 
'W' in room temperature water for 24 hrs. After seeds soaked 
for 24 hrs., I planted the three seeds soaked in cold water in 
one and three/fourths cups of American Gro soil, one inch below 
soil level.  I did the same with seeds soaked in room 
temperature water in another identical pot.

III.  Analysis of Data: 

My data showed that the seeds soaked in room temperature water 
didn't begin to grow until after day six.  Seeds soaked in cold 
water didn't sprout until after day nine.  Seeds soaked and 
watered with cold water grew no more than three-quarters of an 
inch.  The seeds soaked and watered with room temperature water 
grew up to six and one-quarter inches.  The seeds soaked and 
watered with the room temperature water continued to grow well 
and nearly quadrupled the height of the seeds soaked and 
watered with cold water.

IV.  Summary and Conclusion: 

In conclusion, the plant seeds soaked and watered with room 
temperature water grew best.  Therefore, I accepted my 
hypothesis which stated that seeds soaked with room temperature 
water will grow taller.  I Learned from this experiment that 
seeds soaked and watered with room temperature water grew well, 
as opposed to ones soaked and watered with very cold water.

V. Application: 

This experiment would probably be most beneficial to gardeners, 
farmers, florists, and lawn care specialists. If a gardener or 
florist needs flowers or plants quickly, they could speed up 
the growth process by soaking the seeds and watering them with 
fairly warm water.  Farmers doing this could enhance the growth 
process of foods, which could result in more sales and may help 
prevent possible starvation.



Title:  The Search for the Perfect Wax

Student Researchers:  Chris Warkocki and Mitch Allen
School Address:  Eisenhower Middle School
                 3525 Spring Creek Road
                 Rockford, IL 61107
Grade:  8th Grade
Teacher:  Mrs. Hutchinson

I. Statement of Purpose and Hypothesis

In aggressive inline skating, people wear a type of inline 
skate made to do tricks.  Some tricks for the street division 
are to grind or slide down rails and curbs.  To grind curbs and 
rails you must put wax on it to help you so you don't slip or 
stall on the surface.  We are searching for the best type of 
wax that will help a person slide down a curb in inline skates.  
Our hypothesis states that a wax we made of synthetic wax, 
paraffin wax, and lip balm would work the best for grinding 
down a curb.

II. Methodology

We tested our hypothesis by first cleaning the grinding 
surface.  We scraped off the old amounts of wax still deposited 
with a paint scraper.  Then we applied two coats of the 
homemade wax.  Then we did a makio grind where the sole of one 
foot is on the curb and the other foot is extended forward and 
grabbed.  We did this five times on the curb with the homemade 
wax on it.  Each time we measured how far we slid down the 
curb.  Next, we reapplied the wax to do five mizou grinds where 
the front foot is grinding on its sole and the back foot is 
grinding with the sole of the foot facing you and the curb 
corner is in between the middle two wheels.  It looks like an 
upside down T on the curb.  Then we cleaned the surface and 
applied two coats of Land 'O' Ledges synthetic wax.  We 
repeated the different grinds over again.  Next, we cleaned the 
surface again and applied paraffin wax and did all the grinds 
over again for that wax.  Last of all, we thoroughly cleaned 
the surface and did the grinds five times again with no wax on 
the curb.

All the materials we used were: a pair of aggressive inline 
skates, paraffin wax, synthetic wax, homemade wax, curb, ruler, 
and skill.

Some variables we controlled for in this project were the 
amount of wax placed on the grinding surface, the speed at 
which we hit the grind, the type of grinds, the surface, and 
the skates we used.  The manipulated variable was the kind of 
wax used.  The responding variable was the length of the slide.

III. Analysis of Data

After all the data was collected, we averaged the five 
measurements for each wax.  Without any wax, the average slide 
length was 131 cm for the mizou grind and 120.25 cm for the 
makio grind.  With paraffin wax, the average slide length was 
184 cm for the mizou grind and 204.25 cm for the makio grind.  
With the synthetic wax, the average slide length was 189.75 cm 
for the mizou grind and 194.5 cm for the makio grind.  With our 
homemade wax, the average slide length was 221.75 cm for the 
mizou grind and 238.75 cm for the makio grind.  We could slide 
further with our homemade wax.  

IV. Summary and Conclusion

Our homemade wax worked well and had the longest grind length.  
When we looked at the measurements we could see that the 
homemade wax was the best wax to use if you want to grind 
longer and farther.  Therefore, we accepted our hypothesis 
which stated that a wax we made of synthetic wax, paraffin wax, 
and lip balm would work the best for grinding down a curb.

V. Application

It has been an old question of the inline skaters regarding 
which wax works the best.  After our experiment, we have an 
idea that our homemade wax is better than synthetic and 
paraffin wax.  Later, we will have to do more experiments on 
many different types of waxes.



TITLE:  An Infinite Number Of Monkeys . . . A Study Of Random
        Word Generation

STUDENT RESEARCHERS:  Brian Curtis, Katherine Oates, Christine
                      Teebagy
SCHOOL ADDRESS: Belmont High School
                221 Concord Ave.
                Belmont, MA 02178
GRADE: 11, 12
TEACHER: Paul Martenis, plmartenis@aol.com

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

After studying randomness, we began to think about the 
statement, "If an infinite number of monkeys were typing on an 
infinite number of typewriters throughout eternity, eventually 
one would type the works of Shakespeare."   We wondered about 
random word generation and how likely it would be that 
something coherent would result from this process.  We decided 
to run a program that would randomly generate 2, 3, 4, 5, and 6 
letter words.  We hypothesized that in the same number of 
trials for each length of word, there would be varied results 
in the number of English words.  We believed that our results 
would show an exponential relationship between the number of 
letters per word and the number of English words contained in 
the 5000 word sample.  

II.  METHODOLOGY:

Materials

Compaq Presario 586/75mhz w/8mb RAM
Hewlett-Packard Deskjet 540 Printer
WordGen 1.0, a random word generation program by James Knight
Paper 
Highlighter
Variables
The only variable in our experiment was which letters the 
computer picked.  

Procedure

1.  We obtained all of the above materials.
2.  We decided to run the program using two, three, four, five, 
and six letter combinations.
3.  We ran the program, and printed the results using 
WordPerfect 6.0 for Windows.
4.  We looked through the printed sheets, line by line, and 
highlighted English words.
5.  We tallied the English words that we found for each of the 
data sets (printouts).  
6.  We repeated the procedure, this time having the program put 
one and only one vowel in each combination.
7.  We printed these results and searched for English words.
8.  We analyzed our data, drew conclusions and made graphs.

III.  ANALYSIS OF DATA:

Our results were very close to what we expected.  The number of 
English words we found decreased as the combinations of letters 
got longer.

There were two areas of this project that were prone to error.  
The first was the fact that we may have missed some words when 
we were reading over the printouts.  We were very meticulous, 
but it would be nearly impossible to find every word.  The way 
to eliminate this problem would be to make a computer program 
to find the words for you.

The other reason error may have occurred is that the random 
number generator on the computer, which runs the program, is 
not entirely random.  This probably does not have much effect, 
and it would be nearly impossible to fix the problem.

IV.  SUMMARY AND CONCLUSION:

Our results support our hypothesis very strongly.  We had 
expected the number of English words we found to decrease close 
to exponentially as the combinations got longer.  This is in 
fact what happened.  We did not know what to expect in terms of 
numbers, so we only had a hypothesis as to what the curve of 
the graph would look like.  Because our results support our 
hypothesis, we accepted it.

V.  APPLICATION:

This project has application in the field of randomness and 
probability.  With better equipment and more time, the 
experiment could be useful in the field of linguistic studies.  
It would be interesting to see what the results would be if the 
experiment was run on a very powerful computer and millions of 
trials were done.  

The project will help people understand that a random event may 
produce an outcome that does not seem random.  The study of 
randomness is difficult because there are so many different 
factors to take into account.  A project like this one can give 
a better understanding of randomness because of its simplicity.

MATH SECTION


TITLE:  The Relationship of the Volumes of Pyramids and Prisms   

STUDENT RESEARCHER:  John Daly and Corey Sanders  
SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John we. Swang, Ph.D.

I.  STATEMENT OF PURPOSE AND HYPOTHESIS: 

The formula for finding the volume of a pyramid (V=1/3xbxh) 
states that the volume of a rectangular pyramid is 1/3 of the 
volume of a rectangular prism (v=lxwxh) with the same length, 
width, and height.  We would like to find out if the formula is 
true.  Our hypothesis states that the volume of a pyramid will 
be 1/3 of the volume of a rectangular prism with the same 
length, width, and height.

II.  METHODOLOGY:

First, we wrote our statement of purpose and review of 
literature on pyramids, prisms, and Cavalieri.  Then we cut six 
rectangular prisms and six rectangular pyramids out of wood.  
After the solids were cut, we put them into sets of two with 
one rectangular prism and one rectangular pyramid.  In each 
set, the rectangular pyramid and the rectangular prism had the 
same length, width, and height.  

We then took a jar and set it in a plastic box.  Next, we 
filled the jar up with water to the very top.  After that, we 
took the pyramid and placed it in the water in the jar. Since 
the pyramid would displace water equal to its volume, we took 
the water that over-flowed into the box and pored it into a 
graduated cylinder.  Then we measured the volume of the water.  
Each milliliter marking on the graduated cylinder is equivalent 
to one cubic centimeter (ccm).  The volume of the displaced 
water was equal to the volume of the pyramid. 

Next, we filled the jar back up with water to the very top.  
After that, we took the rectangular prism and placed it in the 
water in jar.  Since the prism would displace water equal to 
its volume, we took the water that over-flowed into the box and 
pored it into a graduated cylinder.  Then, we measured the 
volume of the water.  Each milliliter marking on the graduated 
cylinder is equivalent to one cubic centimeter (ccm).  The 
volume of the displaced water was equal to the volume of the 
prism. 

After that, we took the volumes of the pyramid and prism and 
placed them in a fraction.  The volume of the pyramid was the 
numerator and the volume of the prism was the denominator.  
Then we divided the volume of the pyramid by the volume of the 
prism, to find out if the volume of rectangular pyramid was 1/3 
of the volume rectangular prism which had the same length, 
width, and height.  we repeated each step for each set of 
pyramids and prisms. 

III.  ANALYSIS OF DATA:

We found that the volume of each pyramid was about 1/3 of the 
volume of a prism with the same length, width, and height. The 
reason that it wasn't exactly 1/3 is due to experimental error.

                                 Trial 1

                                          Ratio of Pyramid
        | Pyramid Volume | Prism  Volume |    to Prism    |
Test 1  |     218 ccm    |    668 ccm    |     1/3.06     |    
Test 2  |     206 ccm    |    687 ccm    |     1/3.34     |
Test 3  |     204 ccm    |    670 ccm    |     1/3.28     |
Average |     209 ccm    |    675 ccm    |     1/3.22     |
                        
                                 Trial 2
 
                                          Ratio of Pyramid
        | Pyramid Volume | Prism  Volume |    to Prism    |  
Test 1  |     111 ccm    |    375 ccm    |     1/3.37     | 
Test 2  |     123 ccm    |    426 ccm    |     1/3.46     |                                                          
Test 3  |     147 ccm    |    434 ccm    |     1/2.95     |
Average |     127 ccm    |    412 ccm    |     1/3.24     |

                                 Trial 3

                                          Ratio of Pyramid
        | Pyramid Volume | Prism  Volume |    to Prism    | 
Test 1  |      71 ccm    |    233 ccm    |     1/3.28     |
Test 2  |      97 ccm    |    237 ccm    |     1/2.44     |
Test 3  |      98 ccm    |    236 ccm    |     1/2.41     |
Average |      89 ccm    |    235 ccm    |     1/2.64     |

IV.  SUMMARY AND CONCLUSION:

We accepted our hypothesis which stated that the volume of a 
pyramid would be about 1/3 of the volume of a prism with the 
same length, width, and height.

V.  APPLICATION:

The information we found could be used to find the volume of a 
room that is in a pyramid shape so that you would know how 
strong of an air-conditioner to get to keep it cool.

SOCIAL STUDIES SECTION