A Few Announcements and Activities

Math Tutor: Math assistance is available with Ekta Misra.

E-mail: ektamisra@hotmail.com

Phone: 248-650-1010 or 313-802-1519.

Note: I asked Ekta to keep records of who she sees, how often, and how long. Seeing her counts for fulfilling or exceeding attendance requirements in this class. So for those of you who joined us late, or who plan to be absent, seeing Ekta is one good way of protecting your grade (remember, attendance counts 50%).

MPE: Unless you have already taken—and passed—the Math Proficiency Examination, you will need to take it to pass and be graded in this class. Date & Time: Friday, Dec. 16, 6:00 p.m., Rm. 679, Student Center Bldg.

Catching Up? We are considerably behind in our work. Three hours is simply not enough. Next week we have a test on the material we were supposed to cover so far, but we have only covered a fraction of it. How shall you overcome this problem?

You will need to catch up on your own, in part.

Meet with Ekta as often as you can.

We can have an extra session this Friday, 6-8, 68 Manoogian, provided we have enough takers. So, if you plan to attend, sign up today.

I shall be available, in my home, for tutoring this Saturday, 12-8. If interested, sign up for this today. Note: Cancel or re-schedule at: 248.427.1957 or mnissani@cll.wayne.edu

Here is a map:

 

 

 

 

 

Circles and Formulas

I realized the magnitude of the task ahead of us last session, when most of you failed to grasp the ideas of a formula and of figuring out the circumference of a circle. These ideas are so central to your success that we have no choice but to address it at length. We are going to take as long as necessary to make sure that you understand how to figure out the circumference of the circle and—far more important—how to plug in values in a formula.

First we need to be familiar with a few terms:

Radius is the line connecting the center of the circle to a point on the circumference

To get a diameter, you simply continue the line of the radius to the other side of the circumference. Hence, for any given circle, the diameter is twice the radius.

Please fill in the ???:

 

 

 

Relationships between Radius and Diameter

Radius

Diameter

Radius

Diameter

?

17 in

 

1,000,000 mm

3.43 miles

?

¼ mile

 

55 km

?

 

7 yards

Now, sometimes we need to figure out the length of the circle itself. That is, if I start walking around the circle at one point, and go all the way around, how long would I walk? Another way of saying this is asking: How long is the circumference of that circle?

Now, my long suffering friends, this poses a terrible problem for us, because we can’t measure the length of a circumference with a ruler. So we have to find a roundabout way of doing this. But, ah, you say, if we could only stretch that odd shape to form a line, then we could measure it with a ruler. Well, we can almost do that, by placing dental floss on the circumference, stretching it into a straight line, and then measuring it with a ruler. Let’s try that for a few circles:

Now, let’s write down the information we collected in the form of a table:

  Circumference
Circle A  
Circle B  
Circle C  

 

You realize immediately that the bigger-looking circle has, naturally, a bigger circumference. You realize too that this method is rather inaccurate and inconvenient! We need, and can, do better than that. How?

The trick here is to realize that we don’t need to measure the circumference directly. Rather, we see plainly that the longer the diameter, the longer the circumference. So, maybe, if we could measure the diameter with a ruler, we could multiply it by some number and find out the length of the circumference. Let’s try this on our circles:

  Circumference Diameter Diameter X ? = Circumerence
Circle A      
Circle B      
Circle C      

 

 

Well now, these are, in part, the mysterious origins of the formula:

C = 3.14D

Now, let’s practice its use. Any time we are faced with a problem of this sort, we:

Jot down the formula first (C = 3.14D)

Then we get the numbers we need for the formula (e.g., if they give us radius here, we find out the diameter).

Now we plug in the numbers.

Finally, we calculate.

Let’s practice by writing down the formula and then using it to fill in the blanks in the table below:

Formula is:

 

 

 

  Radius Diameter Circumference
Circle A 5 in ? ?
Circle B ? 17 cm ?
Circle C ½ in ? ?
Circle D ? ? 34 km
Circle E      
Circle C ½ in ? ?

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