![]() The software units for picture computation are written in the programming language C. Therefore, combinations of these functions can be easily realized by simple multiplications. The main idea is that these functions deliver zero values at the position of the geometric object. Students, Health Headquarters, News, Activities), and more. These functions can be easily combined to create more complex geometric structures. Math formula for making a kaleidoscope image movie While waiting for the movie to load, play the quiz game. He developed a set of mathematical functions to visualize basic geometric objects (line, circle and arc) in a surrounding colorful field. ![]() So the original shape is right over there.Christian Gaier creates colorful geometric-mathematical pictures and videos as hobby. I've looked into MathML.Net, but I don't need the equation editor, so I was hoping to find something. Since MathML does not seem to be supported yet by most browsers, I need a tool to dynamically convert the formulas to transparent images. ![]() The basic function for one circle is a cone with the apex pointing down and compressed up. I have a website that will need to display some mathematics (mostly fractions and square roots) in HTML. Original right triangle, if you just took a cross section of it that included that line you Cybernetic Kaleidoscope 1 A superposition of many circles. The center of the base, it's gonna go through So draw the cone so you can shade it and we can even construct the original so that, well or we canĬonstruct the original shape so you see how itĬonstructs so it makes this, the line, that magenta line, is gonna do this type of thing. ![]() Shade it a little bit so that you can appreciate that this is a three dimensional shape. And this is the tip of the cone and it's gonna look just like this. The radius of the base and it is three units. So what you end up getting is a cone where it's base, so I'm shading it in so that hopefully helps a little bit, so what you end up getting is a cone where the base has a So let me shade it in so you see the cone. It's a cone and if I shade it in you might see the coneĪ little bit better. The shape that I am drawing? Well what you see, what Take a section like this it would have a little smaller circle here based on what this distance is. This and then you'd have another thing that goes like this and so if you were to Look at the intersect so it would look something like this. Note that this is a parametric equation the first half gives the x -coordinate and the. Here’s the expression that generated this curve: (cos ( t) + cos (6 t )/2 + sin (14 t )/3, sin ( t) + sin (6 t )/2 + cos (14 t )/3). Put a few pieces of tape on the backs of the mirrors to hold them together. But then this end right over here is just gonna stay at a point because this is right The curve has a fivefold symmetry, which you can clearly make out in the image at right. Place the three mirrors together as shown, using the long side of each mirror. This would be like taking a magazine (not quite 2D, but pretty flat and thin compared to the lengths and widths. I'm gonna rotate it around the line, so what's it gonna look like? Well this and this right over here is gonna rotate around and it's gonna form a circle with a radius of three, right? So it's gonna form, so it intersects, if that was on the ground It is not exactly changing a 2d object into a 3d object, it is more related to rotating a circle and putting billions and billions of these circles together to form a sphere. So once again this is five units, this is three units, So that's our magenta line, and then I can draw my triangle. So let me draw this same line but I'm gonna draw it at an angle so we can visualize the whole In three dimensions, what I'm going to do is try to look at this thing in three dimensions. Put some object such as a coin, or the small pieces of colored paper in the resealable bag (keep them in the bag) on the white cardboard inside the kaleidoscope. Hold the kaleidoscope above the white cardboard and look down inside it. I encourage you to think about it, maybe take out a piece of paper, draw it, or just try to imagine it in your head. Hold the kaleidoscope in your hand and look through it at objects around the room. It around this line, what type of a shape am I going to get? And I encourage you - It's going to be a The line that I'm doing as a dotted magenta line. It in three dimensions around this line, around I'm gonna take this twoĭimensional right triangle and I'm gonna try to rotate That this length is five units and now I'm gonna do Width right over here is three units and let's say Well what do I mean by that? Let's say I started with a right triangle. Two dimensional shapes in three dimensions. Visualizing what happens if we were to try to rotate What I want to do in this video is get some practice
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