Five minute presentation on Second paper

A short written exam - 45 minutes max

A small problem solving project

Last class

We went through the pendulum problem, solve it Excel, and learned to compute the period and frequency.

We discussed the Final Exam and condcuted the course evaluation.

A link on how to prepare Power Point Presentations

No Class, work on your paper and presentation

Oil Spill Experiment. Are you ready for it ?

Oil Spill Movies and Pictures Note that all images are stores in the pics directory (appears at the end of the list)

Instructions for Paper 2

Paper (2) Reminder. A sample paper on how the references should be marked in the paper was given.

Completed the experiment and find the mathematical model using MovieMaker.

Here are the four short videos you created for the long and short pendulums. Note: we used two cameras, so you have two versions of the same motion to choose from. These are in MP4 format. You need to convert them to the format of the MovieMaker (.wmv) as before and find the period. Make a table in Excel that contans the time and distance from the center at each of the extremes and the center.

Short Pendulum Video 1

Short Pendulum Video 2

Long Pendulum Video

Long Pendulum Video 2

Studied the Pendulum Motion. Setting up an experiment to find the mathematal model for this motion.

We assumed that the pendulum was in vaccum. We concluded that the length of the string that holds the weight, the angle that we start the motion, and the mass or more precisely the gravity seem to be important in the period and frequency of the motion. Our next job is to find out how these are related.

We determined that the length has a direct relation with the period, i.e. we said the linger the length the longer seem to be the period (longer it takes for the weight to come back to its origin once it is released). We see to agree that the larger the mass, the shorter the period. I.e. the heavier the mass is the shorter it takes for the weight to have a full periodic motion.

We refert to a web page: Pendulum to see how we did. Can we come up with the same formul;a using the techniques we learned in class this semester?

We used the MovieMaker to extract the clips of the short videos. Then we decided to choose a location on the CD we wish to consider for marker to determine when the CD has a full turn (rotation). For example we lined up the edge of the red marker with something on the background. Everytime the edge met the mark on the background, we call it one complete turn and wrote the time of clip down. At the end we had a table similar to the one below. We subtracted the time between each time that the mark has come to the same point as the period. Period is the time it takes for one full rotation to happen. We observed the full rotation several times and every time recorded the time of the clip.

Time of Clip Time diff (period)

0.27 0

1.01 0.64

1.66 0.65

2.31 0.65

For example the time of the first clip was 0.27 and the time that we saw the same CD at the same location next time was 1.01 sec, so the difference between 1.01 - 0.27 = 0.65 sec. The average time for each rotation is 0.65 sec. That is the period. So, in average it took about 0.65 second for one full rotation. We want to compute the frequency, which is the number of rotations in one second. So, if it took 0.64 sec to get one rotation, how many rotations will happen in one second? f = 1 (sec)/0.65 (sec/rotation)

The answer is f = 1.538 rotations/second.

We converted the videaos from MP4 to MovieMaker .WMV format. We uploaded the videos in the MovieMaker and then used the clips to find the time where the object appears at the same location. Then found out how long it took for an object to come back at the same location again. This was the period.

We will work on analyzing the short videos.

Here are the short videos you made . Save your video before you run it.

Xilisoft Video Converter This converter works well and you will get 3 minutes of conversion for free. Our videos are very short.

We will have Mrs. Antoinette Sithole (pronounced Sit oh lay) as our Guest Speaker. Mrs. Sithole is Sithole is museum educator and curator of the Hector Pieterson Museum in Soweto, Johannesburg, South Africa. "Children, Apartheid, and Education: A Look at South Africa Then and Now"

We discussed the SunSpot problem and conducted some computations in Excel to determine the SunSpor period.

We recorded some short videos of some periodic motions. We will analyze them in the next class.

We will use the cameras to take some short videos and measure timing of events.

Learn about Microsoft MovieMaker. We plan to use it to solve some problems.

Using a camera to capture some motions (short movies) and importing these short files into the MS MovieMaker. Extracting frames and determining the time in sec it takes between one event to another. For example, how fast can you raise your hand from your side to full extension above your head.

A You Tube Tutorial for MovieMaker

First we will finish the periodic lab handout.

Periodic Function Hand-out

Periodic Function Hand-out-Solution

Click Sunspot Data to download the data. Open the file in Excel and follow the Handout for the Sunspot Data Analysis to learn about the behavior of the data.

We discuss how the image processing techniques you have learned so far could be used in the Microscopy Lab.

Periodic Function Hand-out

Periodic Function Hand-out-Solution

We talked about periodic functions, Sin and Cos, and generated some angles, converted them to Radian, and then computed their Sin and Cos in Excel. We plotted the Sin and Cos and made some observations. More detailed observations will come in the next class.

Tour of Microscopy Lab - Class meets in the Microscopy Lab at the class time.

We would work on Excel again.

We learned to generate 50 random points for x between 0-11, and 50 random points for y between 0 to 8.5. We used the =rand()*11 to generate the points for x and =rand()*8.5 to generate the points for y. Once we generated these points in column A and column B of the Excel sheet, we plotted the values. We adjusted the Max and Min on the x and y axses so they correctly show the 11 and 8.5 as max, respectively. The data seemed to be distributed uniformly in the 8.5-by-11 rectangle.

We created 500 data points the same way.

Then we inserted the image of one of the unknown shapes we had, the one with straight edges, and study how the distribution of data points are on the shape. We used 50 data points and coutned the number of points that fell inside the shape. We computed the ratio of that number to the total number of points used (50 in our case) and calculated the area using the ratio.

For Assignment - you will use Excel and the image you used in Assign (4) to compute the area. Note, you will generate random numbers just like you did in class to do the computations.

A picture of the shoe with a great hint Here

We started working on solving the problem we had thought about during weekend. We looked at the image of the key (The first image in the set of images we took from different objects) that was taken with putting the paper under it. Now we don't the paper to use as a reference. How do we measure the area now?

Two groups had two different approach: One team took a picture of the key and had a ruler next to the key. THis helps them set a scale for the measurement of the lengh using the ruler, then they used the scale to draw a polygon around the key and found out what the surface area is.

The second team used a different approach. They first measured the edge of the key to find out how long it was and then used the scale tool to set the length of that edge to number of pixels. Then used that pixel scale to find out how many pixles were in the length and height of the image. Then the number of pixels inside the key were found, and ratio was computed, which can be used to compute the area.

We took the discussion outside due to Fire Drill. Both teams shared the $1M prize for finding the best answer.

Quiz 6 - download this image (Right click here to save) on your PC. Then answer the questions on the Quiz sheet.

Finishing the computation of the areas of the objects we took pictures of in class.

Here is a good example: How Big is Antarctica?

Preparing to design an experiment to compute the area of an oil spill case

Here is how you can download ImageJ on your own machine ImageJ full package Note this is a free software provide by NIH.

We used ImageJ to find the area of the shape with straight edges and the are of the shape that didn't have straight edges. In case of the object with straight edges, we used the Polygon Slection to draw a polygon around the shape and Used the Analyze->Measure tab to count the number of pixels in that shape. Then we did the same thing for the regular paper on which the object was drwan. We calculated the ratio of the number of pixels inside the shape to that on the paper. Since we knew the paper was an 8.5-by-11 inch size, then we computed the area of the paper and multiply that by the ratio to get the area of the object.

For the shape without straight edges, we used the Freehand Selection tool and went around the shape and counted the number of pixels in the shape and on then on the entire paper. We used the ratio to calculate the area.

In the second part of the class we took the picture of some objects and upload them on our server, then we computed the area for these objects as a team. You can access the images at All Images taken in class today

You have an assignment for next Wed.

Here is a good example: How Big is Antarctica?

Exam(1) grades and discussions

Reminding students to complete the Library Survey on ASULearn page

We will use the ImageJ Image Processing Tool to measure the area of the two shapes.

Here is how you can download ImageJ on your own machine ImageJ full package Note this is a free software provide by NIH.

Looking at the way we can measure the area using image processing techniues.

Using ImageJ to measure area

Here are the images of the two shapes you had experienced with in class: Click here to get a list

Quiz

We created 100 and then 500 random numbers between 2 to 4. We discover two Excel functions that would generate random numbers.

rand() would generate a random number between 0 to 1 and randbetween(x,y) would generate an integer between x and y randomly. Since we wanted a number other than integer, we used a technique to create a non-integer number between 2 to 4. So, we have to map the random numbers that rand() is producing between 0 to 1 to a range between 2 to 4. So, 0 gets mapped to 2 and 1 gets mapped to 4. How do we do this?

which means, Desired random number = rand()*(4 - 2) + 2

We tried this and genrated 100 and then 500 random numbers and used a scatter plot to show their distribution. The numbers seemed to be distributed randomly.

Then we asked how good this randomness was? Students suggested that if the number of random numbers within any equally spaced range is the same, then the random numbers are pretty random. We used grids of 0.1 aprat on the plot and counted the number of dots in each range. They were very close. So the random numbers you have generated in Excel or pretty random.

Paper (1) due by Midnight

We combined the three spread-sheets we had for our past three experiments:

1) The first one we had where we covered the entire surface of the paper with lentils,

2) The one where we used 50 and 100 lentils and spread them randomly, and

3) The last one where we used a little (about 1/2 cup) lentils and a a little more than the amount used the first time (about 1 cup) and every time dropped the lentils randomly.

Then on each of the sheets, we computed the Mean -(+) 1STD, 2STD, and 3STD. we found that there is a large difference between the estimated value when we covered the entire surface and the one when we dropped the lentils randomly. We discussed the cause of the error. Here are what students found out:

1) Lentiles were bouncing off the paper,

2) Lentiles were getting out of the paper, so maybe if we had boundaries there was better results,

3) Lentils were not the same size,

4) The height where we drop the lentils were not always the same.

We learned that we can solve a problem different ways. It is important that we look at the source of errors and look into improving on those errors.

Here the source of errors were:

1) Lentils were not droped randomly due to the bouncing from the surface

2) Either the counting or weight were not accurate

3) Lentiles were coming out of the paper on edges.

4) what else ?

The experiment with 50 or 100 were not precise, so we decided to use 1/2 cup of lentils and drop them randomly on the paper, then weight those that fell on the unknow shape and then the total to get the ratio. We repeat this experiment three times and record our data. We use an Excel Spread-sheet (click Here to download and enter the weights) to compute the area of the unknown shape.

We will do the same thing with a cup full of lentils. We will drop them randomly, record the data in an Excel Spread-sheet and compute the area.

Let's summarize our learning so far.

The next thing we want to do is to create a Monte Carlo simulation in Excel.

We discussed that spreading lentils over the entire area of the paper and then weighting them was a bit complicated. We started introducing the idea of Monte Carlo Simulation, where instaed of coveriong the entire paper, we picked 50 lentils and drop them randomly over the page. Some of these lentils were on the unknown shape and some outside of it but still on the paper. So, we can find the ratio of these two and just like we did before compute the area of the unknown shape using the ration. We repeated the experiment with 50 lentils 3 times and recorded the data. Then we used 100 lentils and repeated the experiment three times and recorded the data. We need to put all these data in an Excel spread-sheet and do all the calculations. (click Here to download

Today we collected the weight data you had collected for the inside and total weight of the lentils on the unknown shape to the total. We put our data in an Excel Spread-sheet and conducted some calculations. Here is the link to the Excel Data File. In this spread-sheet we computed the:

The way our data is stored in the spread-sheet, we have, somthing like this:

Col A Col B Col C Col D Col E Col F Col G

============================================

Team Win Wtotal Ratio Est Area cm^2 diff diff^2

We computed this using this formula in the Excel spread-sheet:

For example to computer the first ratio, which is stored in cell D2, we used the formula "= B2/C2" in the cell D2. Firt of all "=" means expect a formula, and then it tells where to get the values used in that formula. Since we stored the Win (weight inside the shape) in column B from B2 to B8 and stored Wtotal (total weight) in column C from C2 to C8, then we use the address of the cell to compute each of the ratios. We learnied to copy cell with formula in it to the cells below it instead of typing the formula in each cell one at the time.

After we computed the Ratio, now we need to find the area of the regular size paper (8.5"-by-11") so we can use it to compute the area of the unknown shape. We went to cell A12, B12, C12, and D12 and typed in each, heading of W, H, Con, Area respectively for the Width, Height, Conversation Factor from inch to Cm, and Area. We know Width is 11", Height is 8.5", and Conversion Factor is 2.54. So we went to the cells, A13 and typed the width 11, in cell B13, height 8.5, and in cell C13, conversion factor 2.54. Then we went in cell D13 and put the formula for computing the area of the regular size paper: "=A13*B13*C13*C13"

I am sure you know why we used C13 twice. Remember that you have to convert the height and the width to Cm, by multiplying each of them by 2.54, that is why.

Ok, now you have the Area. We will use this Area and the Ratio to find the area of the unknown shape. This computations are done in column E. So go to column E2, and use this formula "=D2*D$13". Note that we stored the value for Area of the paper in D13. In the formula we used D$13, to make sure when we copy cell E2 to E3 to E8, D13 always stays the same.

By typing "=D2*D$13" in cell E2 and pressing Enter, this formula will be computed. Then you can copy this cell to E3, E4, ..., E8 so the estimated area for the unknown shape is computed.

To computer Standard Deviasion, we need to find the difference between each of the estimated areas and the mean of the estimated areas. So, we first need to compute the average for the estimated areas.

In Cell E9, that in the blank cell right in the column where you have stored all the estimated areas, type "=Average(E2:E8)". Average is a funtion that is already pre-defined in Excel. So, you are giving it a range of values in cell E2 to E8 and will ask Excel to compute that average for you. We will use the cell address of the average value to compute the differences.

Go to cell F2 and there type "=E2-E$9". once agian note that we have used $ sign with E9. One you typed this formula, press Enter and then copy the cell in F2 to F3, F4, ..., F8.

We need difference to the power of 2 in the calculation of Standard Deviation, so go to G2, and type the following formula: "=f2*f2" or "=f2^2". They both produce the same thing. Then press Enter. Now that you have the difference square value in cell G2, copy that cell to G3, G4, ..., G8. Once this is done, we need to compute the sum of all these values for the STD formula.

Go to cell G9, and there type "=sum(G2:G8). This sums all the values in column G2 to G8. Now that we have the Sum, we can compute the Standard Deviation using. Let's store the value for STD in G13. So go to G13 and type "=sqrt(G9/7)". Note that sqrt is a pre-defined function in Excel that computes Square-Root of a value.

Ok. Now you have the Mean and Standard Deviation for the experiment you have conducted. Express the Estimated area using 1STD, 2STD, and 3STD

Learning to search the Internet and online resources for material related to the first paper.

Learning to search the Library records and resources for our research paper.

We will meet at the lobby of the ASU Library at 8:50. We will learn to search the ASU resources.

We looked at a new unknown shape which was very hard to break into smaller known shapes as it didn't have straight edges. You used larger rectangles in the middle, and then smaller and smaller squares in tighter spaces. Then you calculated the area. Since the shape didn't have staright edges, there was no way you could fit smaller shapes everywhere.

Then we used a new technique. We spread lentils over the entire paper where the shape was drawn. We tried to spead the lentils such that they are evenly spread on the paper without sitting on each other. We then slowly took the lentils which were on the paper but outside the shape and use a scale to weigh those lentils. Then we used the scale to weigh the lentils that had covered the shape itself. We know have the weight of the lentils which had covered the shape and we could compute the total weight which was the weight of the two groups.

Total weight = (the weight of lentils that had covered the shape + the weight of the lentils that were outside the shape but on the paper)

R = Ratio of the weight inside / total weight Since we know the paper on which the shape was drawn was an 8.5" * 11" then we could find the total area. A = 8.5*11 = 93.5 in-square

Then we can find the area of the shape using the ratio and this area:

Area of unknown shape = R * 93.5 in-square.

Learn about the oil spill in the sea and how the area of the oil on the sea can be estimated.

Continue with the measurement of the area for unknown shapes. We are going to measure the area of the shape from last class, but this time use two other techniques.

Then we will see how we can use the area of an unknown shape that is not easy to break into regular shapes.

0. Collects the facts together. In the example on the Quiz, we were told the round sections were semi-cricle. Also, we knew all the edges were straight lines.

1. Using proper scale for measurements. In our case since the shape drawn on the paper was small, we used Cm instead of inch.

2. Didn't count the missing value in our calculations. One of the teams didn't have their measurement, so when we computed the Mean, we only used the data from 6 teams and also divided the sum by 6 to compute the Mean for the 6 teams which had data.

3. We didn't consider the ourlier until we found the source of error and calculated the correct value.

4. We used the largest error to estimate the value using the Mean +(-) error. Thus, we didn't take the average of the error values.

5. We decided to represent the values with some number of decimal points and kept that consistent throughout the calculations.

6. Check your answer. Does it make sence. You can use a rough estimate by fitting a rectangle around the shape as one rough estimate.

Here is what we did in class. We finished the calculations for computing the area of the unknown shape which we were able to break into smaller known shapes. We then callculated the Standard Deviation as a representative of the error. We wrote the three ranges:

[Mean - 1STD , Mean + 1STD], 4 out of 6 of our estimated areas fell in this range.

[Mean - 2STD , Mean + 2STD], 5 out of 6 of our estimated areas fell in this range, and

[Mean - 3STD , Mean + 3STD], all estimated areas fell in this range.

We looked at the The definition for STD . We counted the number of estimated areas that fell in the above three ranges. Although we had a small number of calculations we were able to see the distribution of these values.

Quiz(3) - Find the Mean and Standard Diviation for the estimated area of an unknown area that we measure in 6 teams during the class.

We ask each student to divide the given unknown shape into smaller known shapes in three different ways. Then we ask that students to calculate the area as a team using three of these strategies. Then we ask each team to report the Mean of the three values they have calculated. We identify one outlier, and ask the team which reported that result to check. We found out that the area of the semi circles were not divided by two. Once that correction was made the 6 values were more reasonable. We computed the largest difference between the Mean and the 6 estimated areas. Then we reported the area as:

We looked at different strategies that was used to break the unknown shape to the smaller known shapes to see whether we can say which one was more efficient.

We estimated the area of a shape that could be broken down into some smaller regular shapes. We had 6 teams estimating the area. Most teams divided the shape into 3 triangles. We wrote the 6 estimated areas on the board. We had a suggestion that the average of the values would be a good estimate. We realized that one of the values was very high (outlier). We asked the team with that answer to check their answers. The team found out that they hadn't used the correct conversion factor to convert inch to cm. After the correction was made, the team reported a value that was more reasonable, so we included that value in our calculations. We found the Mean for the six estimates. Then we computed the relative difference between all the values and the Mean. Then we talked about Standard Deviation as a way to estimate the error. We computed that value using:

Basically we computed the difference ebtween each of the estimated values and the Mean, and then computed raised each to the power of 2, and sum them up. At the end, we computed the square root of the sume/6, where 6 was the total number of areas we had estimated.

Before we leave, we computer the Mean-STD and Mean+STD and learn that a good number of areas fall within this range.

Discussion of the solution to Assignment (3)

Zero Gravity - NASA

Digital Cameras - A Beginner's Guide, Bob Atkins

Measuring the are of an unknown shape, which can be broken into regular shapes.

Discussions of the Three Cups of Tea and Greg Morgenson's talk on previous day. Listing some of the problems the new generation will face with.

Discussion of the solution to Assignment (2)

Exponential Function

Radioactive Decay Formula

Continue with the Handbook on Problem-Solving Skills

Labor Day Holiday

Handbook on Problem-Solving Skills

Introduction to Problem Solving Strategies

Some sample problems

We discussed the problem where 4 people had to cross a bridge in 17 minutes when they all had a different individual crossing time of 10 min, 5 min, 2 min, and 1 min. Two people at the time can cross and one has to always hold the one and only flashlight they have.

We then discussed the jealous husband problem with three couples. These couples have to cross a river.

Some sample problems

We talked about the importance of working on your courses starting the first week of school. We solved the sailor, goat, wolf, and cabbage problem using a diagram. Initially, most students indicated that they didn't understand the diagram. But once notations were added (G for goat, W for wolf, C for cabbage, and S for sailor) and we explained that the arrows indicates what direction the baot was moving, everyone understood the diagram, hence the solution.

We then presented the rabbit, carrot, sailor, and dog problem. The problem seemd similar at first, but we had removed the constraint that only two items can travel in the boat.

Introduction: Presentation - Problem Solving in Math and Science

We talked about importance of identifying problems correctly and solving problems correctly. Alos, we talked about the READ IT strategy.

You are to work on the sailor, goat, wolf, and cabbage crossing the river.

W went through the READ IT strategy.

Syllabus - Introduction

Notes: Problem Soving in Science and Engineering