Μαθη...μαγικά : Γεωμετρικά μοτίβο που παράγονται απο την κίνηση μεμομονωμένων σημείων!!

Τετάρτη 29 Ιανουαρίου 2014

Γεωμετρικά μοτίβο που παράγονται απο την κίνηση μεμομονωμένων σημείων!!

Here a line of fixed length is moved along the edge of an ellipse, tracing out a collection of new shapes. Consider the area of the shape traced by a point p units from one end of the line and q from the other. Holditch’s theorem, regarded as a milestone in the history of maths, tells us this area is less than the area of the ellipse by at least π×p×q. Curiously, this formula holds not just for an ellipse, but any closed curve. [more] [code]

Μεταβλητό ευθύγραμμο τμήμα που κινείται με τα άκρα του,σε μια έλλειψη
Another interesting property of the logarithmic spiral is revealed if you roll it along a horizontal line. This animation shows the curves traced by points on the spiral, and note that the very centre follows the path of a straight line. The angle between this line and the horizontal is called the pitch of the spiral, and for our spiral galaxy the pitch is around 12 degrees. [more] [code]

Another interesting property of the logarithmic spiral is revealed if you roll it along a horizontal line. This animation shows the curves traced by points on the spiral, and note that the very centre follows the path of a straight line. The angle between this line and the horizontal is called the pitch of the spiral, and for our spiral galaxy the pitch is around 12 degrees. [more] [code]

Λογαριθμική σπείρα

Draw a straight line, and then continue it for the same length but deflected by an angle. If you continue doing this you will eventually return to roughly where you started, having drawn out an approximation to a circle. But what happens if you increase the angle of deflection by a fixed amount at each step? The curve will spiral in on itself as the deflection increases, and then spiral out when the deflection exceeds a half-turn. These spiral flourishes are called Euler spirals. [code]

Δείτε πως 8 σημεία που κινούνται πανω σε 8 κύκλους και δίνουν την αίσθηση ενός τρισδιάστατου ορθογωνίου παραλληλεπίπεδου
A simple animation showing how connecting points rotating on circles at different phases can create the illusion of a 3D figure moving, rotating and skewing. [inspired by] [code]