The National Student Research Center

E-Journal of Student Research: Multi-Disciplinary

Volume 5, Number 2, January, 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:

Artificial Sparks and Natural Lightning
A Study of the Strength of Spaghetti
Which Brand Of Paper Towel Absorbs The Most Water?
Does The Number Of Coils Affect The Strength Of An Electromagnet?
To Germinate Or Not To Germinate: Is That The Question?
The Effect of Vitamins on Zinnias
Agars, Percolation, and Critical Probability

Math:

Does Pi Always Equal 3.14 No Matter How Large Or Small The Circle?

Social Studies:

What Students Know And Feel About Nuclear Weapons
What Students Know And Feel About Racism

SCIENCE SECTION


TITLE:  Artificial Sparks and Natural Lightning

STUDENT RESEARCHERS:  Jacob Brauer, Mike Greene, Maire Soosaar
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:

We wanted to find out more about lightning and sparks as 
fractals.   We sought to learn if there is a difference in 
fractal dimensions between artificial sparks (electric sparks 
made by humans) and natural lightning bolts.  Our hypothesis 
states that natural lightning and artificial sparks have 
approximately the same fractal dimension. 

II.  METHODOLOGY:

Using 1000 speed film in a 35 mm camera on a tripod, we 
attempted to take photographs of sparks created by a Van de 
Graaff generator and a Leyden jar.  We set up the generator in 
a dark room, opened the shutter (it was on a manual setting) on 
the camera, and waited for a spark.  After we saw a spark we 
closed the shutter.  We repeated this procedure using a Leyden 
jar.  We took 12 photographs of each.   We planned to scan the 
photographs into the computer and find their fractal 
dimensions.

We also scanned pictures of natural lightning and artificial 
sparks from National Geographic into a computer.  Using Image 
1.44  we isolated and 'cleaned' each bolt by "reducing noise" 
and "skeletonizing."  "Reducing noise" eliminates stray marks 
while "skeletonizing" reduces each image to a width of one 
pixel.  We undertook this process so that all of the images 
would be reduced to fractal edges: the thickness of a bolt 
effects it fractal dimension.  Then using the box and fast 
circle methods in Fractal Dimension 5.1, we found the fractal 
dimension of each image.  In the box method, we used the powers 
of two from 2 to 128 pixels.  We used these numbers because 
they are the same ones that the fast circle method uses, and 
they provide a good spread of data points on a log (# of 
rulers) v. log (ruler-length) graph.

III.  ANALYSIS OF DATA:

Our photographs did not come out.  Consequently we had to find 
and fix existing photographs of artificial bolts in order to 
have enough data to make a conclusion.  Here are all the fixed 
sparks and bolts we investigated and their fractal dimensions:  

          Fractal Dimension of Artificial Sparks:

NAME                BOX METHOD                FAST CIRCLE
Spark 1                .832                      1.087
Spark 2                .955                      1.015
Spark 3               1.001                      1.066
Spark 4                .861                      1.065
Spark 5               1.049                      1.059

Average                .940                      1.058
Range               .832-1.049                1.015-1.087 

          Fractal Dimension of Natural Bolts:

NAME                    BOX METHOD             FAST CIRCLE
Natural Bolt 1             1.095                  1.263
Natural Bolt 2              .957                  1.078
Natural Bolt 3              .958                  1.041
Natural Bolt 4             1.046                  1.268
Natural Bolt 5             1.037                  1.056
Natural Bolt 6              .974                  1.179
Natural Bolt 7              .920                  1.108
Natural Bolt 8              .968                  1.078

Average                     .993                  1.091
Range                    .920-1.095             1.041-1.268

The box method calculated fractal dimensions that were 
generally lower than those of the fast circle method.  In 
several instances, the box method results were less than one.   
We believe that this is because the box method does not start 
the grid in the same place each time.  The box method is 
inconsistent.  This is especially relevant when dealing with 
large boxes. 

From the data, we see that artificial sparks and natural bolts 
have approximately the same fractal dimensions.  Bolts that 
were photographed from miles away and sparks and bolts that 
were photographed from a few feet away had approximately the 
same fractal dimensions.  For example Natural Bolts 1 and 2 
were photographed from several miles away while Natural Bolt 6 
struck a tree just a few hundred yards away from the camera.  
We also read that natural lightning discharges hundreds of 
millions of volts, while the largest man- made spark we 
investigated (Spark 5) only discharged 1.3 million volts.  

IV.  SUMMARY AND CONCLUSION:

We found that artificial sparks and natural lightning have 
approximately the same fractal dimension.   Because of this, we 
accept our hypothesis.  But our data was not limited to proving 
our hypothesis - we also have two secondary conclusions.  The 
fact that lightning has approximately the same FD no matter 
what the distance, reveals  that lightning is self-similar, and 
therefore fractal.   From what we have seen, voltage does not 
significantly affect the FD of sparks and lightning.

V.  APPLICATION:

The fact that lightning is self-similar and fractal, may help 
scientists in the future understand how this phenomenon occurs.  
Does lightning involve a random walk?  According to National 
Geographic, one bolt of natural lightning contains more 
electricity than all the U.S. power plants combined.  Lightning 
could be a great source of energy.

TITLE: A Study of the Strength of Spaghetti

STUDENT RESEARCHERS: Liza Blair, Adam Ertas, Sara Field, 
Caitlin Gauthier, Lindsay Kurahara, Ben Lepesqueur, Tom 
Lepesqueur, Brittney Lewellen, Katherine Littlefield, Joshua 
Miller, Kieran Murphy, Brent Parker, Saeger Philpot, Lilly 
Stolper, Eric Taylor, Emma Turnage

SCHOOL: Sant Bani School
        19 Ashram Rd.
        Sanbornton, NH 03269 
GRADE: 6
TEACHER: Robert Schongalla


I. STATEMENT OF PURPOSE AND HYPOTHESIS:

Our sixth grade science class wanted to learn about how to test 
products and learn about the process of science. We decided to 
test the strength of spaghetti by seeing how many pennies it 
would take to break different types and amounts of spaghetti. 
Our hypothesis stated that the thicker the spaghetti, and also, 
the more pieces we used, the more pennies it would take to 
break the spaghetti. 

II. METHODOLOGY:

Our teacher bought three types of round spaghetti: Angel Hair 
(1 mm thick), Regular (2 mm), and Perciatelli (3 mm). We 
tested the spaghetti by placing each end on two 2x4x10 inch 
blocks. The blocks were 18.5 mm apart so that the ends of 
each piece of pasta were flush with the outside edge of the 
blocks. An 8 oz. paper hot cup was hung from the middle of the 
spaghetti using a paper clip. We worked in pairs and did five 
or six trials for each type and amount of spaghetti. We put 
pennies into the cup until the spaghetti broke and then 
recorded the results on data sheets. We summarized the results 
on a class data table by throwing out the high and low values 
and averaging the three or four middle numbers for each test. 

We did two series of tests. For the first series, we tested 
one through five strands of each type of spaghetti. After 
graphing the data and discussing our findings, we predicted how 
many pennies it would take to break six through ten pieces of 
each type. Then, we did the second series of tests on six to 
ten strands of each spaghetti. Because of the results, we 
decided to check the weight of pennies. We weighed about three 
hundred and fifty pennies of different dates.

III. ANALYSIS OF DATA

For the first series of tests (one to five pieces), the class 
found that the average number of pennies needed to break 
spaghetti was 18 for Angel Hair, 21 for Regular, and 31 for 
Perciatelli. In general the slopes of the graphs increased 
steadily as we expected. Our class was very surprised with the 
results of the second round of testing (six to ten strands). 
We found that the average number of pennies needed to break 
spaghetti was only 11 for Angel Hair, 19 for Regular, and 29 
for Perciatelli. This means that compared to the first round 
of tests, the number of pennies needed to break the spaghetti 
in the second round of tests was lower by 35% for Angel Hair, 
9% for Regular, and 6% for Perciatelli. 

We have four theories about why the results of the second 
series of tests were so different: 1) There was about one week 
between the first and second series of tests. We think that 
moisture or temperature could have affected the spaghetti 
because of where it was stored. 2) In the first series of 
tests, we used 1996 pennies. However, for the second round, we 
used older pennies of mixed dates. Our class discovered that 
pennies from 1956 to 1981 weigh an average of 3.1 grams and 
from 1983 to 1996 they weigh an average of 2.5 grams. This 
means that it took fewer pennies to break the spaghetti in the 
second series of tests because all the pennies 1981 and older 
were 0.6 g heavier on average. This was a real source of error 
in the data. 3) The Angel Hair is the thinnest pasta and we 
found it hard to work with. It often sagged under the weight 
of the pennies in the cup and sometimes slipped down between 
the blocks. 4) Some of the error is probably due to 
miscounting.

IV. SUMMARY AND CONCLUSION:

We accepted both of our hypotheses that the thicker spaghetti 
would be stronger, and that higher the number of pieces, the 
more pennies needed to break it. While we found important 
differences between our two series of tests, we were able to 
trace much of the error to moisture and temperature differences 
in the spaghetti, differences in penny weight, differences in 
procedure, and counting mistakes.

We recommend that future experiments should include more 
trials. It would be very important to use pennies of the same 
weight. It would be interesting to test the effect of 
moisture and/or temperature on spaghetti strenght. Does 
spaghetti strength change over time when an opened box sits 
out? We recommend that the blocks be placed 8-12 cm apart -- 
just wider than the cup -- so that sagging of thin spaghetti 
won't be so much of a problem. It would be fun to test other 
types of pasta, too.

V. APPLICATION

Finally, while the results of our study might only interest a 
spaghetti manufacturer, we learned a lot about how science is 
done. It would be easy to test other materials or products 
using the same process and methods that we used for testing the 
strength of spaghetti. 



Title:  Which Brand Of Paper Towel Absorbs The Most Water? 

Student Researcher:  Brian Ailes                    
School Address:  Hillside Middle School            
                 1941 Alamo
                 Kalamazoo, Michigan 49007
Grade:  Seventh 
 Teachers:  Barbara A Minar

I.  Statement of Purpose and Hypothesis: 

I wondered which brand of paper towel would absorb the most 
water.  I compared Brawny, Bounty, Hi Dry, Green Forest, and 
Job Squad paper towels to see which paper towel absorbs the 
most water.  My hypothesis stated that Bounty would absorb the 
most water.

II.  Methodology: 

I tested my hypothesis by doing my experiment in a lab with all 
the materials I needed.  The materials I used were: paper 
towels (5 types), beakers, 100 ml of water, graduated cylinder, 
paper, and a pen.  First, I poured 100 ml of water from the 
graduated cylinder into the beaker. Then I opened the package 
of paper towel and took one sheet and dipped it into the beaker 
of water by the corner.  Then I pulled it out of the beaker by 
the corner and let it drip all the excess water.  Next, I 
measured the amount of water left in the beaker by pouring the 
water back into the graduated cylinder.  Then I subtracted this 
amount from 100 ml and recorded the difference on a data chart.  
I repeated the above steps again on the same brand of paper 
towel.  Finally, I repeated steps 1-6 for each brand of paper 
towel. 

III.  Analysis of Data: 

My data shows that Bounty absorbed an average of 20 ml of 
water, Brawny absorbed an average of 13 ml, Job Squad absorbed 
an average of 30 ml, Green Forest absorbed an average of 13 ml, 
and Hi Dri absorbed an average of 10.5 ml of water.  My data 
showed that there are some very cheaply made paper towels and 
some better quality paper towels.

IV.  Summary and Conclusion:

The brand of paper towel that absorbed the most of the 100 ml 
of water was Job Squad.  Therefore, I will reject my hypothesis 
which stated that Bounty would absorb the most water.  Bounty 
was the second most absorbent.  If I were to do the experiment 
all over again, I would add an extra trial to get more reliable 
results.

V.  Application: 

This experiment applies to the world outside the classroom many 
ways.  One way is that it could save people from wasting their 
money on cheaply made paper towels when they could be getting 
their money's worth with another brand.  



TITLE:  Does The Number Of Coils Affect The Strength Of An
        Electromagnet?

STUDENT RESEARCHER:  Justin Trosclair and Rob Krieger
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 
electromagnets.  We are interested in seeing if the number of 
coils around a electromagnet effects the strength of its 
magnetic for field.  Our hypothesis states that the 
electromagnet with the greatest number of coils will pick up 
the most paperclips. 

II.  METHODOLOGY:

First, we wrote our statement of purpose and then we reviewed 
the literature on electromagnets, electricity, negative and 
positive charges, volts, and amperes.  Then we wrote our 
hypothesis.  Then we wrote our methodology and listed our 
materials.  Next, we conducted our experiment.  We took a nail 
and wrapped a wire around it 5 times.  Next, we connected the 
ends of the wire to the terminals of a 6 volt battery.  Then we 
laid out 15 paper clips and ran the nail over them.  Then we 
counted how many paper clips were picked up and record that 
information on a data collection sheet.  We repeated the above 
steps four more times with a different number of coils 
(10,15,25,30) around the nail.  Then we analyzed our data and 
wrote our summary and conclusion.  Finally, we applied our 
findings to the world out side the classroom.
 
III.  ANALYSIS OF DATA:

Our first electromagnet had five coils and, after six trails, 
it picked up an average of one paper clip.  Our second 
electromagnet had ten coils and, after six trails, it picked up 
an average of one point five paper clips.  Our third 
electromagnet had fifteen coils and, after six trails, it 
picked up an average of three paper clips.   Our fourth 
electromagnet had twenty coils and, after six trails, it picked 
up an average of four paper clips.   Our fifth electromagnet 
had twenty-five coils and, after six trails, it picked up an 
average of three point three paper clips.

IV.  SUMMARY AND CONCLUSION:

The maximum number of coils for optimal functioning of an 
electromagnet using a six volt battery is twenty.  Our 
electromagnets picked up a greater number of paperclips as the 
number of coils were increased up to twenty.  Then the 
electromagnetic force field started getting weaker.   Therefore 
we reject our hypothesis which stated that the electromagnet 
with the greatest number of coils will pick up the most 
paperclips.  More research needs to be done on this topic to 
find the best ratio of coils to voltage to make electromagnets 
more efficient.

V.  APPLICATION:

This information could be used to build stronger electromagnets 
for electric motors, junk yard cranes, and generators for power 
plants.



Title:  To Germinate Or Not To Germinate: Is That The Question?

Student Researcher:  Christopher Borges
School Address:  Westminster School  
                 3819 Gallows Road   
                 Annandale, Virginia  22041
Grade:  8
Teacher:  Cynthia Bombino

I. Statement of Purpose and Hypothesis:
   
I want to find out which method (micro-radiation, freezing, 
vinegar bath, or ammonia bath) would prevent seeds from 
germinating.  I wanted to find out if an exposure to micro-
radiation (power 10) for 10 seconds, 24 hours of freezing, a 
one hour vinegar bath, or a one hour ammonia bath would prevent 
seeds from germinating.  My first two hypotheses stated that 
the micro-radiation and the ammonia bath would prevent seeds 
from germinating 100%.  My third hypothesis stated that the 
vinegar bath would prevent the seeds from germinating by 50% 
(half of the seeds would germinate and half would not).  My 
fourth hypothesis stated that the freezing would not affect the 
germinating process.

II. Methodology:
   
 Materials:
    100 seeds (any kind)                       Paper towels      
    Microwave                                  Tin foil
    Freezer                                    Dark place
    Vinegar                                    Paper plate
    Ammonia                                    Spray bottle
    Beakers or containers of any kind          Water

Independent Variable:  Micro-radiation - 10 seconds
                       Freezing - 24 hours  
                       Vinegar bath - 1 hour
                       Ammonia bath - 1 hour
                       No treatment  

Dependent Variable:    Seed germination

Procedure:
        
(1) Put 20 seeds in a beaker so that none are on top of 
another.  Then place the beaker in freezer for 24 hours.  (2) 
Fill one beaker with 1 1/2 cups of vinegar and another beaker 
with 1 1\2 cups of ammonia.  DO NOT PUT SEEDS IN YET.  (3) 
Place one damp paper towel on a sheet of tin foil and set it 
aside.  (4) With 1 hour left in freezing, place 20 seeds in the 
vinegar and 20 seeds in the ammonia.  Make sure that none of 
the seeds are on top of another. (You are trying to time it so 
that all of the seeds will be ready at the same time).  (5) As 
the time for the freezing and the vinegar and ammonia baths 
come to an end put 20 seeds on a paper plate.  Spread them out.  
Put them in the microwave (power 10) for 10 seconds.  (6) Take 
all the seeds out and place them on the damp paper towel and 
keep the different seeds separated.  You should have 5 
groupings or divisions: Freezing, Micro-radiation, Ammonia, 
Vinegar, one for the control.  The control group of seed should 
not receive any treatment.  Place another damp paper towel on 
top.  (7) Put the seeds in a dark place and keep the paper 
towels moist.  Do this by spraying water on them twice a day.  
(8) Check on the seeds everyday, but record the results after 7 
days. 

III. Analysis of Data:
    
The data I collected showed that micro-radiation and the 
ammonia bath prevented the germination of the seeds 100%, the 
vinegar bath prevented germination 90%, and the freezing 
prevented germination 80%.  

IV. Summary and Conclusion:  
     
Micro-radiation and the ammonia did prevent seeds from 
germination 100%, the vinegar prevented germination by 90%, and 
the freezing prevented germination by 80%. Therefore, I 
accepted my first two hypotheses which stated that the micro-
radiation and the ammonia bath would prevent seeds from 
germinating 100%.  I rejected my third hypothesis which stated 
that the vinegar bath would prevent the seeds from germinating 
by 50% (half of the seeds would germinate and half would not).  
I rejected my fourth hypothesis which stated that the freezing 
would not affect the germinating process.

V. Application:
    
This experiment could have possible commercial benefits.  At 
least some of the seeds that a person puts in his/her bird 
feeder are guaranteed to fall out. This could be a problem for 
some because then the seeds would grow into weeds and kill 
grass.  This would make their gardens harder to maintain 
because of the constant need for weeding.  An answer to this 
problem is to put seeds in the feeder that cannot germinate.   
Only more experiments could determine which method to use.  
Ideally, the method would prevent seed germination 100% and not 
harm the birds. 



Title:  The Effect of Vitamins on Zinnias 

Student Researcher:  Christine Moundas 
School Address:  Fox Lane Middle School 
                 Bedford, New York 10506 
Grade:  8 
Teacher:  Ms. Russo

I.  Statement of Purpose and Hypothesis: 

I wanted to know the effect of different vitamins on the growth 
of zinnias.  I tested vitamin A, B-12, C, E, and Iron on my 
plants.  My first four hypotheses stated that vitamins A, B-12, 
E, and Iron would be fairly beneficial to plant growth.  My 
fifth hypothesis stated that vitamin C would not be beneficial.  
I believed this because vitamin C is ascorbic acid and I 
thought that this vitamin would burn the roots of the plant.

II.  Methodology: 

First, I wrote my statement of purpose and developed my 
hypothesis from my general knowledge.  Then I got my materials.  
After that I planted my zinnia seeds and started recording 
their growth.  Each individual group contained 12 seeds.  I had 
one control group that had no vitamins.  I used this group to 
compare the rest with.  There were five other groups of plants 
that I used to see the effects of each individual vitamin.  
Each vitamin was a manipulated variable and was the only aspect 
that varied in the experiment.  Every few days I gave the 
plants vitamins.  Depending on the vitamin, I would either 
grind it to administer as a powder or, if it was in a gelcap, I 
would puncture it with a pin and give one drop each.  After the 
vitamins were given, I watered the plants so it could soak into 
the soil.  Each day I recorded the growth of all of the plants.  
After I had enough information, I analyzed it. From my 
analysis, I accepted or rejected my hypothesis and then I wrote 
my summary and conclusion.

III. Analysis of data: 

After many days of observation, I recorded my last measurements 
and began to compare numbers.  The results were very 
interesting.  The control group had an average height of 8 cm, 
the vitamin A group was 7 cm tall, and the plants with vitamin 
B-12 had the same height of 7 cm. The vitamin C zinnias were 
close to dead by the end of my project, but a few seedlings had 
made it up to 2 cm.  The zinnias given vitamin E were 9 cm tall 
and the zinnias given Iron were 10 cm.  The vitamin A and B-12 
have inconclusive results.  The plants are slightly smaller 
than the control, but I can not definitely say if vitamin A and 
B-12 had any effect on the plants.  Vitamin E and Iron have 
shown promising results, with plants that are one to two 
centimeters taller than plants without any vitamins.  The final 
outcome of the plants with vitamin C has made it very clear 
that plants have stunted growth or could die with this vitamin.

IV. Summary and Conclusion: 

For my project, I gave zinnias different vitamins.  I wanted to 
see which vitamins benefited growth.  The zinnias with the 
vitamin E and Iron grew the tallest.  The vitamin A and B-12 
zinnias left me with inconclusive results and I can not 
determine what the effects of vitamin A and B-12 are on plants.  
The vitamin C zinnias were dry and almost dead.  Their growth 
was stunted considerably.  

Therefore, I accepted my first two hypotheses which stated that 
vitamins E and Iron would be fairly beneficial to plant growth.  
I accepted my fifth hypothesis which stated that vitamin C 
would not be beneficial.  I could not accept or reject my 
hypotheses related to vitamins A and B-12 because of 
inconclusive results.

V. Application: 

With this information, it is possible to formulate a vitamin 
based fertilizer. I could have a high iron or high vitamin E 
formula that is proven to be beneficial to plants.  This 
experiment could be expanded upon by using different plants and 
vitamins to determine which vitamins promote the best growth.



TITLE:  Agars, Percolation, and Critical Probability

STUDENT RESEARCHERS:  Beth Kopcke, Ted O'Connell, and Liana 
                      Tenney
SCHOOL ADDRESS:  Belmont High School
                 221 Concord Ave.
                 Belmont, MA 02178
GRADE:  12
TEACHER:  Paul Martenis- plmartenis@aol.com
 

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

We wanted to further investigate percolation.  We wanted to 
find a physical model of percolation since all we had done were 
computer simulations.  We discovered that agar, a gel, is 
formed when agar powder is dissolved in water.  Some powder 
then acts as a bag for the water, forming a solid.  More bags 
are formed off of this original solid, and thus through 
percolation the solid gel is formed.  Through our 
experimentation, we wanted to find the critical concentration 
of powder to water.  The critical concentration (a.k.a. 
percolation threshold) is the lowest ratio of powder to water 
which will likely percolate and form a gel.  Below this 
critical concentration, percolation will almost never occur, 
and above the this concentration, percolation will almost 
always occur.   

II.  METHODOLOGY:

Materials: 

40 test tubes, in racks5g agar powder
1L water, in a beakerhot plate
2 50mL graduated cylinders100mL beaker
25 mL graduated cylinderstirring rod
40 .2g BB's      10 2g masses 
10 5g masses balance
hot hands

Procedure:

1.  We brought 1L of water to a boil on the hot plate.  We 
replaced water lost through evaporation so that the amount of 
water stayed consistent.  We added 5g agar and stirred until it 
dissolved.

2.  We took 1L of a 5g/L solution.  We diluted this with water 
to get solutions of 3.3, 3.2, 3.1, 3.0, 2.9, 2.8, 2.7, 2.6, 
2.5, and 2.4g/L. 

III.  ANALYSIS OF DATA:

We knew that a 10g/L solution would gel.  To zero in on the 
critical concentration, we needed to test lower concentrations 
of agar.  For our first experiment, the concentrations we 
tested were: 5g/L, 2.5g/L, 1.25g/L, and .0625g/L.  To test 
whether these solutions gelled, we dropped a .2g BB into the 
test tube and observed whether it sunk.  It sunk in the 
.0625g/L and the 1.25g/L agars, was suspended in the 2.5g/L 
agar, and didn't sink into the 5g/L agar.  

The next experiment we did involved concentrations of 12g/L, 
6g/L, 3g/L, 1.5g/L, 0.75g/L, and 0.325g/L.  This time the BBs 
sunk in the 0.325g/L, 0.75g/L, and the 1.5g/L agars.  It didn't 
sink in the 3g/L agar and it didn't sink in the 6g/L and the 
12g/L agars.  Using the results of these two experiments, we 
narrowed the range of the critical probability to a little bit 
above 3g/L, and a little below 2.5g/L.  Our final test 
concentrated on the range from 2.4g/L to 3.3g/L, increasing by 
tenths.  We had 4 test tubes of each concentration, 40 test 
tubes in all.  

IV.  SUMMARY AND CONCLUSION:

We found that agar will almost always form at a concentration 
of more than 3.0 g/L.  At a concentration of less than 3.0 g/L, 
the agar will usually not form.  Based on this, we call 3.0 g/L 
our percolation threshold.  

V.  APPLICATION:

To benefit others, we discovered the percolation threshold.  
This can help in future experiments.  Researchers could now use 
different concentrations of agar and not have to say "highly 
concentrated agar" or "lower concentration of agar."  Our 
procedure could benefit them because it is a relatively precise 
way to make agar solutions of specific concentrations.

MATH SECTION


TITLE:  Does Pi Always Equal 3.14 No Matter How Large Or Small 
        The Circle?

STUDENT RESEARCHER:  Paul O'Meallie and Erin Phillips
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 Pi.  Pi is 
the ratio between a circle's circumference and diameter which 
is a transcendental number which equals approximately  3.14159.  
We would like to see if Pi equals 3.14 no matter how large or 
small the circle.  Our hypothesis states that Pi will equal 
3.14 no matter what size the circle is.

II.  METHODOLOGY:

First, we wrote our statement of purpose.  Next, we reviewed 
the literature on the Pi, radius, circumference, circle, and 
geometry.  We then wrote our review of the literature.  From 
our review of the literature, we developed our hypothesis.  
Next, we gathered our materials.  We then developed our 
methodology to test our hypothesis.  After that we each took 
five circles.  We measured the distance from one side of the 
circle to the other side through the center to get the 
diameter.  To find the actual circumference we drew a line on a 
8 1/2 x 11 inch piece of paper.  We then drew a line on the 
edge of the circle we were measuring.  Then we put each line on 
top of one another.  Then we rolled the circle until the line 
on the edge of the circle was again facing the paper and marked 
a line on the piece of paper where the line on the edge of the 
circle was facing.  We used a ruler to measure the distance 
between the two lines on the paper which equaled the 
circumference of the circle.  We divided the circumference by 
the diameter.  This gave us the approximate value for Pi.  
After that we recorded our data on a data collection sheet.  We 
then analyzed our data.  Finally, we wrote our summary and 
conclusion and then applied our findings to the world outside 
the classroom.

III.  ANALYSIS OF DATA:

For circle 1, the diameter was 30.3 cm, the circumference was 
104.3 cm, and Pi equaled 3.44. For circle 2, the diameter was 
25.8 cm, the circumference was 79.7 cm, and Pi equaled 3.12.  
For circle 3, the diameter was 21.2 cm, the circumference was 
79.7 cm, and Pi equaled 3.20.  For circle 4, the diameter was 
20.0 cm, the circumference was 62.7 cm, and Pi equaled 3.14.  
For circle 5, the diameter was 16.0 cm, the circumference was 
49.3 cm, and Pi equaled 3.10.  For circle 6, the diameter was 
8.6 cm, the circumference was 27.5 cm, and Pi equaled 3.19.  
For circle 7, the diameter was 7.2 cm, the circumference was 
24.3 cm, and Pi equaled 3.39.  For circle 8, the diameter was 
6.0 cm, the circumference was 19.0 cm, and Pi equaled 3.16.  
For circle 9, the diameter was 3.0 cm, the circumference was 
9.9 cm, and Pi equaled 3.33.  For circle 10, the diameter was 
2.4 cm, the circumference was 8.1 cm, and Pi equaled 3.35.  The 
average value of Pi for all 10 circles was equal to 3.24 cm.
                   
          |  Diameter  |  Circumference |  Pi  |
Circle 1  |    30.3    |      104.3     | 3.44 |
Circle 2  |    25.8    |       79.7     | 3.12 |
Circle 3  |    21.2    |       68.5     | 3.20 |
Circle 4  |    20.0    |       62.7     | 3.14 |
Circle 5  |    16.0    |       49.3     | 3.10 |
Circle 6  |     8.6    |       27.5     | 3.19 |
Circle 7  |     7.2    |       24.3     | 3.39 |
Circle 8  |     6.0    |       19.0     | 3.16 |
Circle 9  |     3.0    |        9.9     | 3.33 |
Circle 10 |     2.4    |        8.1     | 3.35 |
Average   |            |                | 3.24 |

IV.  SUMMARY AND CONCLUSION:

The average of all the measurements of Pi was equal to 3.24.  
So, according to our data, our measurement for Pi is 3.24.  
From our review of the literature we know that Pi has been 
empirically demonstrated to equal 3.14, but according to our 
data it equals 3.24.  This very small difference of .10 cm in 
our findings is probably due to measurement error on our part.  
Therefore we accept our hypothesis that states that Pi will 
equal 3.14 no matter what size the circle is.    

V.  APPLICATION:

In the world today, shapes and sizes are very important.  We 
use them in construction, electronics, and mechanics.  For 
example, knowing the value of Pi is helpful if a person needs 
to put a fence around a circular yard.  He or she could measure 
the diameter of the yard and know exactly how much fence to 
buy.

SOCIAL STUDIES SECTION