## ยง Interpolating homotopies

- If we have kp + (1-k) q and a contractible space X which contracts to point c, where image of p is x and imagine of q is y, then send the above point to theta(x, 2k) : k <= 1/2 and theta (y, 1-2(k - 1/2))or theta (y, 2-2k)
- This interpolates p---q to x--c--y by using bary coordinates to interpolate along homotopy.