Batch 3 - Class 205 - Planiverse - Astria/Arde

• (MartinShCol 5.4) An equilateral triangle and regular hexagon have perimeters of same length. If triangle has area of two sq units, what is the area of hexagon?
• Answer: 3

• What is dimension?
• How many dimensions does the world around us have?
• How do we know?
• Is it really three dimensional? Can we describe all coordinates with three dimensions? What are those?
• When we see something with our eyes, how many dimensions do we see? By how many independent values can we describe anything that we see?
• How about a point on a given straight line - how many variables do we need to exactly describe the point?
• How about a point on a plane? On a sphere (back to earth?) In space?
• Flatland style planiverse (Edwin Abbott)

• Explain the concept of Planiverse - "on a wall", with gravity
• How do people recognize each other?
• Full shapes and features, but you could still only see a line
• Useful to be able to see on both sides - how would a head "rotate"?
• Alternately, you could have one eye on each side, but then you can't see up
• What choices exist for eyes?
• Lets try and build a full body - what are the considerations?
• Hands? Legs?
• Can we have muscles to move the "bones"?
• What would joints look like?

• Can we have an alimentary canal like we have in humans?
• No, it would create a "hole" through the body and split it into two
• How else can we solve for it? Zipper organs

• What other challenges do you foresee in designing a body?
• How will people walk? How will they cross each other? Transportation?
• One could lie down and the other person can walk over them. But that doesn't scale
• One could build footover bridges - try to construct one. Or balloons

• How would you make transportation?
• You can't use an axle so wheels are hard
• Due to gravity, you now have friction, so flat undersides of vehicles won't do
• Rolling vehicles are not normally used in Arde
• Lets build a house
• Overground houses are hard because they would block the way
• All houses can be built underground - how will the entrance work?
• Swing stairs as a key innovation

• Swing Stairs
• Water Tank
• Collapsible furniture
• Lights
• No nails and saws, since there is no third dimension
• What kind of games could people play?
• One dimensional checkers

• Two dimensional chess as a more sophisticated design

• Orbit of the Planiearth?
• Gravity does not decay by square of distance but by distance => circular orbits
• No seasons
• Sophisticated Machines
• Example of Internal Combustion Engine 
• In 3D world

• In Astria

• Conceptualize some other interesting machines in Planiverse