Color-Pick Applet
When working with computers, we define colors in terms of the amounts of red, green, and blue that the computer uses to generate the color. This can be represented using Hexedecimal code, where two numbers in base-16 represent the amount of each of red, green, and blue. This applet creates a slice of the color spectrum and lets you see where a given hex number lands on the spectrum.
- Imput values in the boxes Blue-1 and Blue-2 to set the amount of blue in the slice of the spectrum we create.
- Press the play button. Let the animation run until it fills the box, then pause it.
- Select Color-Pick Mode.
- Change the values in the four imput boxes to move the dot to the corresponding color in the spectrum.
- You can repeat one or both sections of the exercise for different values of blue, red, and green.
Sine Applet
The Sine Function [y=sin(x)] is one of the basic functons of trigonometry. It is also known as the Sine Wave due to its consistent up-and-down motion as it moves along the x-axis. You may recall from science class that any wave has both an amplitude (the furthest it gets from the axis) and a wavelength (the distance between two consecutive high points of the wave). Investigate below how changing the formula of the sine wave alters it's construction
- Make sure the orange graph, g(x)=sin (x) is showing
- Move the slider for A. Does this effect the amplitude or the wavelength?
- Move the slider for B. Does this effect the amplitude or the wavelength?
- There is one point that does not move, regardless of how you move the sliders. Find that point and theorize about why it is always the same.
Triangle Applet
A triangle is a polygon with three sides. There are many ways to describe and construct the properties of a triangle; here we will be experimenting with one of them and investigating how some triangles, from a certain perspective, actually have four sides.
- Click "Triangle 1" to display the first triangle.
- One important circle in trigonometry is the nine-point circle, which contains the midpoints of each side of a triangle. Click "Nine-Point circle" to display this circle for our triangle.
- The Incircle is that largest circle entirely contained within a triangle. Click "Incircle" to display this circle for our triangle.
- Click "Outer Circle" to display the circle that contains the three vertices of our triangle.
We can now use these three circles to describe each side of the triangle. They have their endpoints on the outer circle, their midpoints on the nine-point circle, and they are tangent to the incircle.
- Click "Triangle Line" to display a line segment and its midpoint. Drag the blue endpoint of this line and observe how the midpoint moves onto the nine-point circle as it aligns with each side of the triangle.
- Now, Click "Four-Sided Triangle to display another triangle. Do not move the vertices of this triangle.
- Use the "circles" and "triangle 2 line" boxes to display the same constructions as before.
- Drag the Triangle line around the circle. Can you find a fourth position where the midpoint of the line touches the nine-point circle?
- Experiment with the triangles and their lines and consider what properties result in a triangle with a "fourth side" and why that might be the case.