sep 20

• Finding the areas of lattice polygons
• Train: how much travelled in 15 min, 30 min, 45 min, 6 min...
• Tree; worm crawls around it. Draw its height, how it changes in time.
• How many maxima? what they correspond to?
• Minima?
• Stone moving game: define a "stationary" configuration. For what number of stones a stationary configuration exists?
• Frog jumping puzzle

Experiments:

• shadows of two pencils: is the distance getting longer as we move them?
• Thee mirrors; rays reflected right back

Homework

• Find the areas of these polygons:
  



• The train (still!) makes 100 miles per hour. Find how many miles it makes in 6 minutes, in 12 minutes, in 21 minute...
  



• A caterpillar climbs a tree. Here is the plot of her height. Can you draw the tree?



• We take some stones and do the following operation: take all the stones from one of the 5 slots and place them one by one on the other slots, clockwise. The we take the stones from the next slot and repeat...
  We call a configuration stationary if after one steps it repeats itself: for example, 4,3,2,1,0 is a stationary configuration. Or 1,0,0,0,0 is.
  Can you find other stationary configurations?