2. A double helix in real space A helix with radius R and pitch Pis described by the following parametric equations: x(t) = R cos(2nt) y(t) = R sin(2nt) z(t) = Pt = 2.1 Projection of a helix on a plane We want to visualize a helix as seen from the side (since this corresponds to the experimental geometry used by Franklin and Gosling, see Fig. 1). Draw the projection of the helix described by the equations above onto the (x,z) plane, showing on your drawing what the lengths R and P correspond to. 2.2 Zig-zag approximation We approximate the projected helix by a zig-zag pattern. This pattern is formed of a series of segments, each of them tangent to the projection of the helix at one of the point where it crosses the z-axis (i.e. one of the points for which x = 0). We call d the distance between two adjacent parallel segments, and a the angle made by these segments with the x axis. Express a and d as a function of P and R. = 2.3 Double helix What new geometrical parameter (in addition to a and d) needs to be introduced if we want to describe a double helix instead of a single helix? 2. A double helix in real space A helix with radius R and pitch Pis described by the following parametric equations: x(t) = R cos(2nt) y(t) = R sin(2nt) z(t) = Pt = 2.1 Projection of a helix on a plane We want to visualize a helix as seen from the side (since this corresponds to the experimental geometry used by Franklin and Gosling, see Fig. 1). Draw the projection of the helix described by the equations above onto the (x,z) plane, showing on your drawing what the lengths R and P correspond to. 2.2 Zig-zag approximation We approximate the projected helix by a zig-zag pattern. This pattern is formed of a series of segments, each of them tangent to the projection of the helix at one of the point where it crosses the z-axis (i.e. one of the points for which x = 0). We call d the distance between two adjacent parallel segments, and a the angle made by these segments with the x axis. Express a and d as a function of P and R. = 2.3 Double helix What new geometrical parameter (in addition to a and d) needs to be introduced if we want to describe a double helix instead of a single helix