## Using Mathematics in Fossil Reconstruction

### An activity for upper level students

This activity from a SCIMAST professional development event sent the participants on a mathematical exploration in a local natural science museum.

A display at the Texas Memorial Museum on the University of Texas at Austin campus presents several wing bones of a pterosaur believed to be the largest flying animal that ever existed-Quetzalcoatlus northropi (Qn). The museum's reconstruction of the animal's wing incorporates fragments, an intact humerus and several bone pieces that were found in the Big Bend National Park in Texas in 1971. How would scientists predict the pterosaur's probable wingspan from these pieces?

Data from similar pterosaurs found throughout the world were available from museum sources. These provided a glimpse of the creatures' proportionality and helped the students construct a table that compares wingspan and humerus lengths.

Taking the two variables provided, length of humerus and total wingspan, students were able to estimate the total wingspread of Quetzalcoatlus northropi. The data plotted on graph paper provided a scatter plot used by the students to determine the line of best fit. This linear regression provided a best estimate from the Qn humerus length. (To determine the entire wingspan, students had to factor in the pectoral girdle-estimated at .5 meter across-that separated the animal's wings.) Other students worked with the data to determine a best ratio, and a few used graphing calculators instead of (or in addition to) the manual plotting.

After determining their predictions, the students went to the Texas Memorial Museum for an up-close view of the wing fragments and the opportunity to measure the reconstructed left wing. While the students' predictions did not exactly match the reconstructed animal (because the line of regression only provides a "best possible fit"), the museum's reconstruction was within the graphed possibilities.

Lingering questions: Why was the estimate not exactly the same as the museum's reconstruction? What does the "best possible fit" mean? Would it be reasonable to use the pterosaur data to estimate the wingspan of a bird or a bat? If we measure our own humerus, and use the pterosaur correlation table, how wide would a human's wingspan be? Is this a realistic estimate? Why or why not?

Pterosaur Humerus Length Total Wingspan
Quetzalcoatlus northropi 54 cm. ???
Quetzalcoatlus sp (small) 24 cm. 600 cm.
Ornithodesmus 20 cm. 500 cm.
Pteranodon 32 cm.
27 cm.
22 cm.
15 cm.
750 cm.
570 cm.
430 cm.
300 cm.
Nyctosaurus 15 cm.
13 cm.
9 cm.
310 cm.
270 cm.
240 cm.
Pterodactylus antiquus 4.4 cm.
4.4 cm.
3.2 cm.
2.9 cm.
1.5 cm.
68 cm.
55 cm.
53 cm.
50 cm.
24 cm.

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