Mastodon Size Math Project
explored by MTH: 160B Students
Spring 2005

Femur Measurements Click to see the project directions. Click to see this group working on the project. Mastodon Projects demonstrate measurements and calculations using linear regression equations. A learning project to provide web pages for our community's better understanding of applying mathematics.




Student Reports:

Robert K.,       Michael T.,       Adam H.,       Elizabeth W.,       Jacqueline R.,       Rebecca A.,       Matthew M.,       Courtney L.,       Joshua F.,       Laura M.,       Allison S.,       Jon G.,       Daniel B.,       Justin F.,       Vance T.,       Michelle M.,       Mirranda T.,       Jaime K.,      
(some reports are in first draft form)


Several mastodon skeleton replicas/reconstructions are represented in the pages of this project.

Illinois State Museum, Mastodon replica.

University of Wisconsin Geology Museum: the skeleton of a 10,000-year-old Wisconsin mastodon

The Perry Mastodon exhibt at Wheaton College in Illinois

University of Michigan Exhibit Museum of Natural History
Museum of Paleontology

Earlham College in Indiana, Joseph Moore Museum of Natural History's Mastodon of 189x.

and MO, exhibited in the Mastodon State Historical Site Museum of Imperial, MO.


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Length and Sholder Height


Robert K.


Mo is the name [our clas has] for the skeleton of a mastodon on display at Mastodon State Historic site in Imperial, MO. The Display is actually a fiberglass replica made up of three different Mastodon skeletons. The objective of this project was to determine the size of Mo and to answer questions such as the sex of the Mastodon.

The first measurements we made of Mo were of the two femur bones. This was done by measuring the anterior and posterior side, as well as the circumference of the Diaphisum, the midshaft section of bone which shows the growth of the animal.
Left Femur


The left Femur had an anterior length of 810mm, a posterior length of 680mm, and a circumference of 530mm. The Right Femur had an anterior length of 710mm, a posterior length of 730mm, and a circumference of 510mm. When the Midshaft Circumference is compared to the data from Tables 2.3 A and 2.3B from the class handouts we can see that the Femur bones of Mo are considerably thicker than most Mastodons, suggesting that he was larger than most Mastodons. Another interesting observation, but one we could find no real explanation for is that the left femur is almost 10cm longer than the right femur. The next Task was to determine Mo’s Shoulder Height and sex.

Next we measured the shoulder height of Mo by using lasers placed level from the shoulder to the toe, and then measuring the distance between the two points. The Shoulder Height of Mo was 2654.3mm. This shows that Mo was a very large Mastodon as Mastodons generally ranged in shoulder height from 2 to 2.6 m, thus placing Mo in the upper realm of Mastodon size (“American Mastodon”.) This can also be used to determine the sex, as Female Mastodons tend to be much Smaller (“Mastodon Americanus”). The Length of Mo also shows how large of a Mastodon he was since the average Mastodon was approximately 4.5m long from Tusk to Tail, and Mo was 5346.7mm long, making him almost a meter larger than most Mastodons (“Mastodon Americanus”).
Right Femur


By Measuring the Femur length, shoulder height, and length of Mo, we were able to determine that Mo was a very large, adult male Mastodon.


The height of a mastadon can be determined by comparing the circumference of its femur to the diapheseal length, which can in turn be compared to shoulder height. By looking at the data from the handouts we can see that The larger the circumference of the Femur, the longer the Diaphiseal Length. The handouts further show that the longer the Diaphiseal length, the taller the Shoulder height. By comparing these two sets of data, we can use the Circumference of the Femur to help determine the shoulder height.




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Courtney L.
The Size Of Mo
When we visited the Mastodon State Historical Site Museum on February 24th, 2005, I was grouped with Danny, Josh, Jackie, and Laura. When we first started sizing up Mo, we were asked to also try and figure out if Mo was a male or female mastodon and also if he or she was left- handed or right-handed. Mr. John Biermann provided important information about mastodons before we began to measure Mo. The anterior is the front of the femur, whereas the caudal refers to the back of the femur. The diaphysial is where the bones fuse with the joints atop the femur. When this fusion occurs, we can tell that the mastodon was done growing therefore being older in age. When we began to measure Mo, we started with the left femur and measured in centimeters and then later converted to millimeters. We found that the cranial portion of the femur measured 800 mm. Next we measured the caudal part of the femur and found that it measured 660 mm. Lastly we measured the circumference of the left femur and found it to be 525 mm.

Next we moved on to the right femur and did the same thing that we did with Mo's left femur. The cranial portion of Mo's right femur measured 780 mm. The caudal area measured 790 mm and the circumference of the right femur measured 510 circumference.

To find Mo's total length we measured from the tip of it's tusk to it's tailbone. When we did this we found the Mo measured to be 5,610 mm. We also measured Mo's shoulder height which we found to be 2,667 mm.
Left Femur

This is a picture of the femur. It shows the diaphysial (top), the caudal side (back), and the anterior side (front).

After we were done finding the required measurements, we tried to figure out the answers to the two questions proposed to us earlier. We started by trying to figure out if Mo was male or female. We compared Mo's information to the mastodon graphs we did individually earlier in the project. Mo's information fit closer to the regression line for the male mastodon graph than the female, so we decided Mo was a male mastodon. Then we moved on to trying to figure out if Mo was right- handed or left-handed. Since Mo is a mastodon, we compared his two tusks. The right tusk was shorter in length than the left, and was also more wore down. We concluded that Mo was right-handed, or right-tusked.


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Mastodon

Michael T.
Mammut Americanum Facts:

Mastodons, mammoths and elephants cannot bend their heads, therefore they cannot see below themselves.

Mastodons, mammoths and elephants have a special stride length that allows them to place the rear foot directly in the front foots track.

Mastodons, mammoths and elephants do not posses collar bones, instead they have evolved special muscle slings and floating scapula to support there front quarters.

Mammoth’s remains have only been found in areas of low tree density as in regions of tundra climate.
Mastodon Femur

·1 Time line: 10,000 years ago
·2 Average height: 8-10 feet
·3 Average weight: 4-6 tons

Left Femurs Right
122 cm Height 114 cm
53 cm Circumference 52 cm
95 cm Anterior 94 cm
95 cm Posterior 90 cm

Length: Cranium to Illeum 128”

Illeum to scapula 110”

Height : Floor to skull 9’3” + (8”—10”)
                  Floor to 4th vertebra 9’3”

Left Leg

Subspecies of mammoth:

·1 Wholly
·2 Jefferson
·3 Colombian


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Left Femur

Elizabeth W.
Mastodon Project Step #3
From my groups research at the Mastodon State Park I believe that I have some good analysis of the information. The first question to be answered is how big is it? From our measurements we discovered that the left femur is slightly large than the right and I have determined that is because it was reassembled from three different mastodons. The measurements were made of the part called the diaphysis from proximal to distal from between the two growth plates, which are the part, were the cartilage has adhered to the bone after the animal has stopped growing on the end. Our measurement of the anterior side of the left femur was 810mm, the posterior side was 680mm, and its circumference was 530mm.
Right Femur

The right femur was measured the same way and we measured it as, the anterior side was 710mm, the posterior side was 730mm,and the circumference was 510.
Height

The shoulder height of the mastodon was measured from the top of the shoulder to the tip of the toe. The measurement that we got was 2654.3mm.
Length

Another measurement that our group decided to get was its length from the left tusk to the left hip the measurement was 5346.7mm.

The last questions to answer are those asked by Mr. Biermann. His questions were what is the mastodon’s sex and was it left or right handed. To figure out if it was left or right handed was not very hard. When we looked at the mastodon it was very clear that the right tusk was shorter and more worn down this told us that it was used more and so that would make it the more prominent tusk. Since mastodons don’t have hands we decided that is how we could tell. The second question was a little more difficult. The right tusk was visibly noticeable but for the sex we did not know what we were looking for. So I tried researching it on-line and through comparisons of other mastodons I decided that our mastodon is a male. The measurements of him compared to other males are very similar.


Step 4

From project one we were able to relate the circumference of the Mastodon's femur to the length of its femur through linear regression. In project two we measured the circumference and the length of its femur and measured the shoulder height of the Mastodon. By relating the knowledge and data we found in project one and two, we can now find the height of the Mastodon from the circumference of its femur. We can find this height by first relating the circumference of the femur to the length of the femur through linear regression. Now that we know the length of the femur and that its length directly relates to its height we can use linear regression to find the relation between length of the femur and the height of the Mastodon.


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Adam H.
Mastodon Project
To measure the shoulder height, a laser level was placed on a photo tripod and shot at the top of the shoulder bone, while another laser was placed on the floor at the toe of the mastodon, shooting opposite of the tripod laser. The toe was not the lowest toe but it was level with the laser on the floor. The measurements of the shoulder height was taken by standing on a ladder opposite of the tripod laser and extending a tape measure from laser (shoulder) to laser (toe). Then we needed to measure from the toe to the floor to make sure we got the measurement to lowest toe to ensure the full shoulder height of the beast. The measurements are:
Leg

Shoulder to toe = 2667mm
Toe to floor = + 140mm
Total shoulder height = 2807mm


The other measurements that were made, consisted of the left femur, right femur, and total length. These were not measured with lasers; instead just a tape measure was used. The femurs (also referred to as the Diaphysial) were measured from the top of the bottom ball joint to the bottom of the top ball joint. The total length was measured from the very rear of the skeleton to the very front, excluding the tusks. The measurements are:

            Right femur height:               Left femur height:
Back       = 780mm                         Back       = 660mm
Front       = 790mm                         Front       = 800mm
            Circumference = 510mm     Circumference = 525mm

Total length = 5610mm

We found, in doing our measurements, that Moe the mastodon was indeed a male. The measurements were found to be closer to the regression graph of a male then that of a female. Also, we discovered that Moe is right handed. The wear on his right tusk, compared to his left tusk, tells us this.

Other Group Members: Becky A., Justin F., David B., Andrew L., Ray P.,
Left and Right


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Rebecca A.
The Size Of Mo
On our field trip to mastodon state park, we took measurements of Mo, the mastodon on display. Included are drawings on what the measurements pertain to and how we got them. In order for our group to get the total height of Mo we had to measure the distance between two lasers, one which was pointed at the top of Mo's shoulder, the other which was pointed at one of Mo's toes. However the one pointed at Mo's toes, did not land at the point where he was closest to the ground, so we had to measure that distance and add it to our height which gave us a total of 2807mm.
Leg

Our guide on the field trip then began to give us the measurements on the femur lengths and circumferences. He informed us that there are two sets of femur lengths for each side (anterior and posterior), he also informed us that the femur length was from the top of one ball joint to the bottom of the other. He then did the mid shaft circumference which was determined by measuring the distance around the middle of the femur. In order to determine the sex of Mo, we plotted the average the lengths of the femur, against the circumference on the regression graph we had previously done for male and females, and determined it to be male, because our plot point fell closer to our male graph.

Then in order to answer the question as to whether Mo was right handed or left, we went with left handed, due to the fact that our data showed the left side to be bigger, we connected that to more use. Which in the end was incorrect; Mo turned out to be right handed due to the fact that his right tusk was worn more. The following is all the data we collected:

Left Femur = 800mm anterior (front)
                  660mm posterior (back)
                  525mm Circumference (mid shaft)
Right Femur = 790mm posterior
                  780mm anterior
                  510mm Circumference

Height = 2807mm
Length = 5610mm


Left and Right In response to our second assignment, How would we determine shoulder height when given femur circumference? My response is to refer back to our regression graphs on femur length and mid shaft circumference, and also our graph on femur length and shoulder height. When we locate where the circumference is on the first regression graph, we can get an idea based on the line of the femur length. We can then take the femur length approximation and use it on the second graph in the same manner which would tell us the approximate shoulder height of the mastodon.


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Matthew M.

Key to Figure 1 (left femur)

a=1120 mm
b=770 mm
c=525 mm
d=800 mm

Individual Question: How can we determine the height of a mastodon given the circumference of its femur?

Thus far into the project, and with the information that we have gathered, I must come to the conclusion that we cannot yet determine the shoulder height of a mastodon given its femur circumference. I reach this conclusion based on the fact that we only have one data point for our studies. I felt displeased with this, and sought out more data, but found only one other data set, and this only gave me femur length; no circumference. When I entered it into my graph, the points created a line contrary to what I had believed would happen: one with a negative slope.

In retrospect, when graphing data of this kind, it is invaluable to have multiple data points.
Length and Height

Key to Figure 2

e=2819 mm
f=5340 mm

I feel that this negatively sloping line given to me is inaccurate. Logically, the longer the femur, the taller the animal would be. I feel that more data is needed to truly complete the graph, and that the two points, when the graph is complete, will fall on opposite sides of a positively sloping line.

I feel that more data must be gathered to make this experiment complete.

Until then, however, my hypothesis is that Mo is a larger mastodon, probably one of the bigger ones. I draw this conclusion from his point on the mastodon table graphing femur length and circumference. His point is one of, if not the, highest point on the graph, and it is fairly close to the line.



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Jacqueline R.

Our College Algebra class went to Mastodon State Park to measure the bones of "MO" the Mastodon skeleton on display. My group consisted of Josh, Danny, Laura, Courtney, and Jacqui. We measured the femurs. On the right femur, we measured the cranial length and got 780 mm. The caudal length of the right femur was 790 mm, and the circumference was 510 mm. On the left femur, we received 800 mm for the cranial length, 660 mm for the caudal length, and 525 mm for the circumference. We also measured the shoulder height and received 2667 mm. When we measured the total left side from the tip of the left tusk to the beginning of the tail bone, we received 5610 mm. From the data we received, we looked on our linear regression lines we made previously, and found out the "MO" came closer to the male line. Also, we believe that "MO" was right-tusked because the right tusk was shorter and worn down.
Length and Height

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Also, based on these projects, we can determine the shoulder height in relation to the circumference of the femur because we can relate the femur circumference to the femur length and the femur length to the shoulder height.



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Daniel B.
At Mastodon State Park I was able to answer different questions through measurements and structures of the bones that made up a mastodon. I determined that Mo was probably right handed because the right tusk was worn down much more than the left, which indicates that the right side was more dominant than the left.
Length and Height

I was also able to make out that this was a full grown mastodon because the joints where the femur meets the ball joint were fused together which shows that the bone was no longer able to expand and grow larger. I went on from here to measure both right and left femur lengths and discovered that the left shaft was 800mm in the front, 660mm in the back, and had a circumference of 525mm. The right femur shaft was 780mm in the front, 790mm in the back, and had a 510mm circumference. These measurements were taken from the femur shaft that does not include the ball joints. The circumference was taken from the center of the femur shaft. The height of the mastodon was taken from the bottom of the foot to the highest shoulder point, which came out to be 2667mm tall. This information along with the femur dimensions were taken and plotted on the previous information about known dimensions of other male and female mastodons. When plotted, Mo turned out to be most likely male. After learning now that Mo is male and right handed we measured the left side from the tip of the tusk to the beginning of the tail bone and learned that an average male, right handed mastodon may have a length of 5610mm.

Question

We can figure out the height of a mastodon based on the circumference of the femur buy comparing the circumference to the length of the femur then by comparing the length of the femur to the height.


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Jon G.
Mastodon Project We can determine the height of a Mastodon from the circumfrence of the its femur by taking the measurements of the femur and pluging it into a linear regression formula. Then with the information from that you get an equation you can pul the data into.

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Justin F.
Based upon the two mastodon projects the height of a mastodon can be determined by its size of femur circumference. Relatively the femur is a little less then 200% of the circumference of the femur.
Length and Height

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Joshua F.
The field trip to Mastodon State Park was in order to take measurements on MO a replica of mastodons from various other digs as well as part from around the area. Laser beams were set up so that one would hit the tallest point in MO’s back. The other laser was at the toe. This is represented in the diagram s point H1-H2 and the measurement of his height is 2667mm. In order to get accurate measurements, I was allowed to get into the gravel pit touch MO. This allowed our group to get three different measurements of the femur. The first three measurements were taken on the left side of MO; this is indicated by the shaded area on the back of the diagram as well as the photo of MO’s leg. The first was the front of the femur shaft, after the fusion points of the bone, this measured 800mm. next the back of the femur was measured at 660mm again in the same area as the front. Finally the circumference was measured at the middle of the shaft to be 525mm. Next the right side was measured to be 780mm, 790mm, and 510mm, respectively. The next task we took upon our group was to measure the length of MO from the tip of the tusk to the base of the tail. In the diagram it is point V-U, and measured 5610mm.
Mastodon

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I Believe MO is a full grown male because upon talking with Mr. John Biermann he informed that the bones were fussed together which is a make in adults. This is similar to a growth plate in humans, once it is closed the bone does not grow, which is evident in adult humans. Once the bones of a mastodon are fused together it is said to be an adult. We plotted the information, measurements of height and the femur, into or models from the beginning of project and found MO more closely fit the regression line of the males opposed to the females. We also concluded that MO was right handed, because his tusk was more worn on the left side and most of the right side measurements were smaller than the left, which we believe is due to extra use of the right side. We can determine the height of a mastodon given the circumference of its femur by plotting the circumference of the femur on our graph that plots the circumference versus the length of the femur. By this graph we can associate the circumference to a point on the regression line. Take that point and reference it to another graph that plots shoulder height versus femur length. This will then give a rough estimate on the height of a mastodon.



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Laura M.
The Size of MO

On February 24, 2005, I went with our class to the Mastodon State Park to make several measurements of MO. I worked with Courtney, Jackie, Danny, and Josh to measure the shoulder height, length of femur shaft, and femur circumference. As well as the total length. All of our measurements are in Millimeters (mm). Here is what we found:

Shoulder height: We found that the height of MO is 2667 mm
front of left femur


We also made several measurements of the femur.

#1.) Left femur, cranial side we found to measure 800mm
            Left femur, caudal side we found to measure 660mm
            Left femur circumference we found to measure 525mm


back of left femur


#2.) Right femur, cranial side we found to measure 780mm
            Right femur, caudal side we found to measure 790 mm
            Right femur, circumference we found to measure 510 mm

To measure the femur length we measured the Diaphysial, (that is the points where the bones had fused to the ball joints, indicating an adult mastodon.)


tip of his left tusk to the tip of the tail bone


Finally we measured the total length of MO. That is from the tip of his left tusk to the tip of the tail bone. We found this length to be 5610 mm.



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Allison S.
Picture Report

Length and Sholder Height

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Jaime K.
Mastadon Project

Mo the mastadon was placed inside a fenced area with a pathway that sloped around the museum. Because of the slope, it was impossible to measure him from shoulder to ground. Instead we measured from the shoulder to the toe (106.5 in) and added a measurement from the toe to the floor (7.5 in). This made for a total of 114in. The next thing that we measured was femurs.


VOCAB:
anterior- toward head
posterior- toward tail
proximal- top
distal- bottom
caudal vertabrae- where the tail begins

Measurements for the left femur, anterior proximal to distal was 123 cm and posterior was 117 cm. the circumference or the distance around the femur was 52.6 cm. For the right femur, anterior was 121 cm and posterior was 117 cm. The circumference was 50.5 cm. The next thing that we decided to measure was from the tip of the tusk to the caudal vertabrae to get the total length of the mastadon. On the right side he is 198 in and the left is 213 in.


Tusk Length Something interesting to point out is that the left tusk is an entire foot longer than the left tusk. John Beirmann pointed out that all animals are dominated by one side just like humans, who we call left or right handed. He said that it was possible to tell by Mo's tusks. They are similar to a pencil. When you use a pencil, it becomes dull and when you sharpen it it becomes smaller. So in Mo's case, he is dominated by his left side and chooses to use it more than the right.



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Vance T.
Measurements of mastodons such as this one at Earlham College in Indiana located in the Joseph Moore Museum of Natural History may add to our study. Jo Mastodon has stayed at Earlham College since 189x.


In March 2005 some pictures were taken and the following measurements were made:

            Left Front Leg Height 279.4 cm

            Left Femur Length 116.0 cm

            Femur Circumference 41.8 cm



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Michelle M.
My measurements of "Mo" taken from the Mastodon State Historic site on February 24th of the the left and right femurs were of the diathesis, the section of bone between the two growth plates that are cartilage that binds to the bone when the animal has stopped growing, from proximal to distal:

1. The anterior measurement was 810 mm.

2. The posterior measurement was 680 mm.

3. The circumference was 530 mm.


Leg

Then there are the measurements for the right femur,which were taken the same way.

1. The anterior meausement was 710 mm.

2. The posterior measurement was 730 mm.

3. The circumference was 510 mm.

Two other measurements taken place were of the shoulder height and the length for tusk to hip.

The shoulder height was 2654.3 mm.

The lenght from tusk to hip was 5346.7 mm


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Mirranda T.


On Thursday February 24, 2005 we went to Mastodon State Park to get the final measurements from "MO". As the pictures show, we found that MO was approximately 281.94 cm tall, which translates to around 9’3", and somewhere around 8.5 tons. We also determined that MO was a right-handed male. He is right handed because you can see the worn spots on his tusk from favoring his right side. And we said that he was male because if MO were female the birth canal would be much larger in order to compensate for giving birth.

As you can see this canal is too small to accommodate a 900 lb. child.


Leg

Then we moved to the rear femur area. The left femur we measured was 53 cm around. The Cephalon, or front side, was 76 cm long, and the Caudal, or back side, was 63 cm long. The right femur was 50.5 cm around. The Cephalon side was 71 cm long as was the Caudal side.

These lines indicate where the measurements were taken from the back left femur.


Leg

This is just showing the points where we measured the height of the Mastodon.
Leg

If you look closely you can see how that far tusk is more rounded on the end, clear evidence that this Mastodon favored the right side.




The next project is about circles
Mastodon Report explored by MTH: 160B Students

Copyright © 2005 with all rights reserved by William V. Thayer