Activity 1

Once we have the required data or information, making graphs, charts, or plots is never a problem for us. With the aide of our modern computers and the numerous calculating and graphing softwares such tasks are usually done efficiently and hassle free. But before the age of even the earliest computers fairly accurate graphs and plots already existed; which is, when you think of it, an amazing feat. I don't know how this plots were made back then, but by simply using the powers of wikipedia we can somewhat get an idea of how scientists back then made use of different types of graphing papers (http://en.wikipedia.org/wiki/Graphing_paper) and odd looking implements (http://en.wikipedia.org/wiki/French_curve) to generate their graphs. In this first activity we recreated a very old plot by using MS Paint and MS Excel.

We took very old handwritten plots from books and journals as far back as the 1920's ,or even older, and scanned them. Now using the select tool of MS paint we took note of the pixel coordinates of all the significant points of the plot. Specifically we took the pixel values of the axis of the plot along with their corresponding physical values indicated on the plot. From these data we obtained the conversion from the pixel values to their physical values. For each tick mark on both axes, we took the difference in their pixel values and also their physical values. From the ratio of these two values we would already have a conversion to use on the curve:

But since the plots were hand drawn these difference in pixel values were not constant, still the variations were not that large so I simply took the average. The more significant concern is that this particular doesn't have an origin with pixel coordinates (0,0) and the plot itself did not even start at 0,0 of the physical values. Also in the image file the direction of increasing pixel value on the vertical was opposite of that with the vertical axis of the plot. Still these problems can be easily addressed by using some basic algebra, point-slope or two-point form of a line, along with some concentration and patience. Doing this I arrived at a modified equation for conversion of the form:

Using the pixel coordinates of the points along the curve in this equation I tried to recreate this plot in MS Excel and compared it with the original. In comparing the two plots we simply use the original scanned plot as the background of the plot in Excel. But upon comparing the recreated curve with the original it was obvious that the two did not match. Then I found out that the x-axis of the plot I chose was not the same through out the plot.

It appears that the origin of the second segment coincided with the 1 value of the first. Also, I found out that the ratio of the pixel values and the physical values of the axes was not the same. I tried to add value of 1 to offset the second segment of the curve and I also used a different conversion for the two parts to improve the appearance of the recreated curve. But as you can see from the figure bellow, though the general shape and trend of the plot was replicated the corresponding points and tick marks did not coincide with the original plot.

After doing a lot of tweaking with the math and even more lucky trial-and-errors I found out that it is not possible to fully reconstruct this plot using this method. So with the permission of my professors I decided to break the curve into two plots and then do the reconstruction.

Finally the recreation is a success...!!! The recreated curve fits very well with the original and even the points and the tick marks are spot on. I would like to give myself a 10 for this but since I was late I guess a 9 would do... hahahahahahhah!!!!!

And since this was a success I have to thank all those who helped me... first my professors Dr. Soriano and Dr. Perez, Thirdy for helping me find this plot, Jica for sending me my files, and Winsome for telling me that I need to sign in before I can do anything with my blog.

Source of Plot: A. Wilmen Duff, et al, "Physics for Students of Science and Engineers", Maple Press Co., York PA, 1926