Graphing Calculator Fun!

I am in a light hearted mood tonight..
If you ever find yourself sitting in math class (algebra I or II, trigonometry, pre-calculus, calculus, etc.) and have a graphing calculator handy then I have a few cool little tricks that you might find fun!

Graphing a Smiley Face : )

I am using a Ti-84 but any graphing calculator will work.
Now, to do this.. I recommend starting with the general equation for a circle.

(x-h)² + (y-k)²= r²
Remember; 'h', 'k' and 'r' are constants.

Texas Instrument calculators will only graph a function entered as a function of x. So you must solve for y.

y = ± √[r²-(x-h)²] + k

The ± gives us either an upside down (+) half circle or a right side up (-) one.
Now, in this form we get to choose some numbers for h, k, and r that give us the desired result on the calculator screen. Each equation will only graph half of a circle and thus you would need the oppisite (negative) equation to complete it... if you were, for example, making the eyes then you would need to do both the negative and the positive. I highly recommend playing around with the numbers to get a feel for it yourself and then designing your own smiley : )
Otherwise here are a few equations that you can plug in to calculator and get a nice smiley face.
To remove the axis you must change the settings format.

Standard window settings:
Xmin: -10 Xmax: 10
Ymin: -10 Ymax: 10
Xscale:1 Yscale: 1

y = + √[4-(x-4)²] + 2
y = + √[4-(x+4)²] + 2
y = -1/2√[30-(x)²] -3 (note: I added the 1/2 in front so as to stretch in the horizontal direction, or the along the x-axis)

Try to be more detailed.. create different kinds of eyes or try to make a nose to match. And when you are done, remove the axes to seee your handiwork in all its glory!

What is my blog all about?

I am here to simply reflect upon the beauties and sorrows of mathematics. To inspire within each of my readers a sense of ultimate truth that is possible to be easily grasped. Am I going to teach you how to do your homework? Yes and no.

In my later entries I might go over some really good study habits that I have accumulated and put together over the many years I have spent learning and teaching math. But truly I will be posting my thoughts and reflections on various perspectives of mathematics, as a discipline having grown and evolved throughout history. Actually, my site, algebraist.org, is being set up to assist with your homework needs. If you have a question to ask me then post it on my site and I will gladly get back to you!
http://www.algebraist.org

Hopefully I will be able to make time to address some common concerns and new age issues. Some examples would be common math disabilities or the latest arguments concerning the necessity to learn fractions.

Also, I love to read. Consequently, I read a lot of math books. When I finish one I will post a little summary and review on its works. Check back weekly (or perhaps even daily) for new posts!

Pure Math Joy

Of the many questions pertinent to life there is one I feel that, at some point or another, every person has asked. Why do we do math?

The answer? Pure Math Joy! We do it because we love it.

Pure math joy is that euphoric feeling of excitement and accomplishment you get when you personally solve that equation for x. It is learning and applying a series of irrefutable truths that organize and make some sense to the confusing chaos of everyday reality. This euphoric feeling is natural and in many ways therapeutic. This is why we do math, and in so doing, our efforts have granted us the miracles of modern genius.

I find that math stimulates the mind and spirit to new levels of awareness, enlightenment, and perspective shifts. It grants one power and understanding. This alone should make it valuable enough to be pursued and explored. Yet it is the simple joy of being productive that taps our inner being (whatever it is that you believe in) and connects with us that makes math such a grand discipline.

This blog is ultimately dedicated to my high-school Pre-calculus and AP Calculus teacher. Without her I would never have taken higher level math in college and discovered the joyful depths of pure mathematics. It is in her great spirit of enthusiasm and the spirit of all math teachers everywhere that I write this blog.