This older version of dart (to me) consisted of a rubber o ring and no spring. Know that other people have movable point darts from other makers as well, so, hopefully will get some info / thoughts from those as well. They where at the time, a bargain set of darts and still are when available, they seem to get made in batches. I aquired some 20 gram darts, going back a few years ago now, as I fancied giving some a throw, then more recently aquired some spring loaded darts, from one of their production runs.Īll of mine have been made and sold by dartsclearance + although thats who made these sets i own, here, am kinda thinking that it will probably be relevent to other makes of darts as well + that other people might share their own experiences, with movable points.Īm going to try and be a bit selective with pictures (as there seems to be a x 3 picture limit per post) so, will be doing more, by way of, writing and might need to make a reply, as an add on, to add pictures, later on.Īm adding a link to their site, so, people can see whats available, if any, its variable what is for sale and they tend to make darts in batches, or, as production runs. I was curious, how the mechanism functioned on these and the basic principals and parts, so, this is partly for anyone else who might be curious. In fact, you can see for yourself: in the applet below, drag the axes' unit (the '1' on the x-axis) left or right, and watch the `a` in the equation change while the parabola's shape remains absolutely constant.Still bit of a work in progress and need to add / take some pictures (so, sorry for any delays) had to modify it a few times as the formating got messed up lol.įirst off wasnt sure whether to put this in the equipment threads, or not. Select either one and click on or near the origin, and see how the same parabola's shape appears to change.ĭownload the file: GeoGebra | Cabri Conversely, look at how different equations can yield the same shape: In the applet below, click on the magnifying glass icon to switch between the Zoom In and Zoom Out tools. The same approach works on a document camera: place the original next to the projected image of a photocopy of itself.) Compare the two transparencies, which seem to have very different shapes, but clearly must represent the same equation. Use another transparency to trace a piece of the projection, like the one below. (Dan Bennett suggests a dramatic illustration of this: make a transparency of a figure like the one above. Visual Arguments: Same equation, apparently different shapes: The reflection property suggests this construction of sorts: Therefore P' is P, and MP is tangent.Įxercise: Prove the reflection property of the parabola, assuming that the angles of incidence and reflection are determined with respect to the tangent to the parabola at the point of incidence. But the only way for P'T to equal P'T' is for T' to be T. Because it is on the parabola, it is equidistant from F and d, so if T' is the foot of a perpendicular from P' to d, we have P'T = P'F = P'T'. Because P' is on MP, it is equidistant from F and T. Indeed, assume MP intersects the parabola at P and another point P'. The key to the proof is realizing that MP must be tangent to the parabola. That this works is readily proved using the above construction, if you assume a basic fact from optics: the angle of incidence equals the angle of reflection. Likewise, a light ray coming in parallel to the axis of symmetry will be reflected to hit the focus. A light ray originating at the focus will be reflected on the parabola and continue in a direction parallel to the axis of symmetry.

Gsp5 moveable points