Maple Leaf
Posted in Uncategorized on 05/21/2010 08:30 am by admin
Find the area of a maple leaf?
Hi, this is a really hard problem for me and I have no idea what to do. I need to find 4 different ways to measure the area of a regular maple leaf with an error not to exceed .5%. I already have the graph paper idea, are there any others? Please help.
You have some options:
1. Take a picture of it using a digital camera, and then use the free program ImageJ* to calculate its area — more instructions given if you’re interested.
* http://rsbweb.nih.gov/ij/
2. As you’ve indicated, trace it on graph paper and calculate the area by counting the number of squares.
3. Trace it on heavy high quality paper, cut it out and weigh it on a balance. Then, weigh a square of known area. The ratio of the two masses will allow you to calculate the unknown area of the leaf.
4. Use the “surveyor’s formula” to calculate the area from its perimeter. Again in ImageJ, click on a number of points on the leaf image, to get the x and y locations of all of the points. Then, visit the web site cited below** to calculate the area of your irregular polygon.
** http://mathforum.org/library/drmath/view/55141.html
Finally, note that this is not a Botany question in the strict sense, even though you’re measuring the area of a leaf — that is, you might get more perspectives if you post to a Mathematics or Engineering section.
Michael Lu at Syncopation Sunday playing Maple Leaf Rag by Scott Joplin
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