Thoughts, opinions, and ideas about Mathematics and other things from a retired teacher.

## Tuesday, October 27, 2015

## Monday, October 19, 2015

### A question for pre-calc students

This question is easily stated, but is it easily answered?

Stay tuned!!

Stay tuned!!

## Monday, October 5, 2015

### GeoGebra or Desmos?

Here is my 3-leafed rose plot in Desmos. Below you will find the same plot in Geogebra. The GeoGebra version, to me, can be presented to students earlier in their math program.

## Thursday, October 1, 2015

### Use truth values wisely!

This blog post is in reaction to Shelby Aaberg's post at Matheleticism regarding defining piecewise functions, Read that posting first! I submit a simple solution that eliminates the complex solution supplied.

All we must do is take advantage of the fact that the truth value "false" yields 0, whereas "true" yields 1, and dividing by zero is undefined. Thus multiplying by the truth value equates to multiplying by either zero or one, and dividing by the truth value goes right along with that. So dividing by the truth value is the same as dividing by either 1 or 0.

The same works at Desmos, as shown in the second graphic below.

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## Tuesday, September 15, 2015

## Thursday, September 3, 2015

### Take it the other way!

Here is a discovery I made while doodling around with GeoGebra. I searched around and could find nothing about it. Perhaps it's new? Who knows. It was new to me!!!

## Friday, August 21, 2015

### If only graph paper were elastic...

One of the troubles trig students sometimes have deals with the amplitude and frequency of a trig graph. One approach I stressed was to recognize that the basic shape of the sine curve, for example, never changed. Just its position.

This is more evident when we look at the sine curves on an elastic graph paper.

In this example, drag the coefficient sliders to new values. You will see that the graph paper stretches or shrinks in each direction so that the graph stays put.

This is more evident when we look at the sine curves on an elastic graph paper.

In this example, drag the coefficient sliders to new values. You will see that the graph paper stretches or shrinks in each direction so that the graph stays put.

Neat, isn't it?

## Tuesday, April 21, 2015

### Students need time to explore

Great mathematical discoveries can be made by students when they have the time to freely explore and "play around" in the world of mathematics. This is just a little example of how perceived complexities can have an underlying common theme. Have fun!

## Wednesday, April 1, 2015

### Ellipse are simple!!

Are you aware that an ellipse is actually a simple object? Take two circles, and have one point on each orbit as below, and just trace the midpoint between them.

## Tuesday, March 31, 2015

### Inscribed angle is half of its central angle!!

You can believe it! Just make sure you know that this is not a proof!! You can drag the points wherever you want before you start. Made in GeoGebra!!! Find my complete file here.

## Sunday, March 29, 2015

### Congruent Chords and Arcs

Hi. I am trying to find a way to combine #GeoGebra files in a version of an online reference book.

Wish me luck. I think PowerPoint

Wish me luck. I think PowerPoint

*might*be good.## Friday, March 27, 2015

## Thursday, March 26, 2015

## Tuesday, March 17, 2015

### The Golden Arches

I have read and heard quite a bit over the years as to the curves in the Golden Arches of McDonald's.

Play around with this. It might clue you in, but it leaves a lot of stones unturned. Just drag the points to locations (anywhere, no special order) along the curve you are investigating, then click "show graph".

## Wednesday, February 11, 2015

### Rectangle approximations for area can be easy

Using rectangles as a tool in approximating areas is as old as the hills, but is brand new to many students and incomprehensible to some people. My position is that by using technological tools such as GeoGebra in a well-designed manner, topics such as this can clarified. This one (full file here) utilizes some features of GeoGebra that I personally just learned about. I hope to improve on it over time. Have fun.

## Tuesday, February 10, 2015

### Is the Law of Sines Mysterious?

By this stage of the year most classes are done with mid-year exams and diving into the second semester. With that in mind, I give this to Algebra II, Trig, and Pre-Calculus students. It relates to the constant referred to in the Law of Sines. Do not click on the "plot spoiler" until you have a good idea as to the meaning of the constant!

## Tuesday, January 6, 2015

### Is it an ellipse?

Is this trace an ellipse? Can you tell?

Take note: the center of the circle rotates once around the origin while the point on the circle does one lap around point E.

More on this type of sketch in the future.

Take note: the center of the circle rotates once around the origin while the point on the circle does one lap around point E.

More on this type of sketch in the future.

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