Freddy: [...] Ladies and Gentlemen, may I present for your intellectual and
philosophical pleasure, the Creature. [...] First, may I offer for your consideration, a
neurological demonstration of the primary cerebeller functions, balance
and coordination. Walk heel-to-toe. Backwards.by The FrankensTeam We found this fantastic math visualizations collection on Tumblr: http://visualizingmath.tumblr.com/archive and become immediately inspired to (re-)create some of the animations in Excel... Then created some new. Here are the examples with downloadable files. ## Perfect visualization of Pi:You can download our Excel version where the circle goes back and forth too. :-) and if you find this intriguing remember to take a look at our Digits of Pi in Excel: fomula challenge and visualization. Inspired by this 6-circle version we created a "playground" in Excel where you can set the number and size of circles and the angle-distance of the dots. Download the 6-circle Excel version with parameters. Download the 8-circle Excel version where you can change the number of circles too. And this is how our improved version looks like: Do you see the optical illusion? You will realize that the rotation changes if you focus on the small circle or the large circle. We created two versions with lots of parameters. ## Trigonometry## CycloidAccording to wikipedia a cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line.(source: Wikipedia)You can download the Excel file and play with the route of the circle - but the most interesting parts are just coming... when a circle rolls within or around another circle.In case of epicycloid the wheel rolls around another cyrcle. (source: Wikipedia)The shape of the curve depends on the ratio of the radius of the two circles. Download the Excel file and play with the radius settings to see how the curve forms. ## EpitrochoidIn case of epitrochoid, the point need not be on the edge of its circle: d is the distance from the center of the exterior circle. (source: Wikipedia)You can play with all the settings in our file: It could be smaller or larger than the radius of the circle, and could also be negative. Just push play to see how the curves form... for example curves like these: Try to find the parameters we used for the above curves. Download the Excel file, where you can see the animations. ## HypocycloidHypocycloid is the trace of a fixed point on a small circle that rolls within a larger circle.(source: Wikipedia)Depending on the starting position of the fixed point, we created two versions. The curve starts from upside position: The curve starts from downside: Download the Excel file to play with the radius settings and see how the curves form. ## HypotrochoidSimilarly to epitrochoid, the point need not be on the edge of its circle: d is the distance from the center of the exterior circle.(source: Wikipedia)You can use the same settings for the radiuses and the distance as for epitrochoid. In our file you can find two animations: when the point starts from up or down position. Here are some examples: ## One trickAll the above illustrations and files use circles. To draw a perfect circle in Excel you need a perfect square plot area and gridline. The easiest way to do it is to add a pie chart-type data series to your scatter chart with {0} value. |