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We ask that you help us in our mission by complying with these Terms & Conditions. We keep our prices low so all teachers and schools can benefit from our products and services. We believe in the value we bring to teachers and schools, and we want to keep doing it. We are a small, independent publisher founded by a math teacher and his wife. See what happens when the two radii are integer multiples of one another. You may even make the inner circle larger than the outter one. It’s super cool, right now it is set to generate the following: You can change the radii of the two circles using their sliders right above the a = slider. On the spirograph, hit the a= play button to watch the small inner circle move around the interior of the larger circle while the curve gets traced out. I botched the math a few times, but that just made the end product better when I finally worked out all of the right triangle trig. They never work that well these days when I by them for my kids, but that didn’t stop me from creating one. You know, those great plastic gears that you put a pencil in and then spin one circle around another. So, then I got really ambitious and decided to try to make a spirograph. Just press the play button beside the a= parameter to allow the circle to roll and trace out the cycloid path: For those of you who are new to Desmos, it can graph just about any 2-D curve and then make it dynamic (in this case by allowing me to dynamically change the domain of the parametric system so the curve is shown tracing itself out). I was testing last Friday and decided I wanted to create a Desmos graph that generated a cycloid (the path a fixed point on a circle traces out as the circle rolls along a horizontal surface). But, the more I use it the more I am convinced that it is one of the greatest tools out there for both classroom demonstrations and outright mathematical investigations. I know I’ve blogged before (yes I did just use that as a verb) about Desmos, this great online calculator.
