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High school geometry is surprisingly useful
It all started when I met this guy Ben, who had made this simple triangle-based strategy game. Only problem was that it didn't work too well, and as a hardcore gaming nerd it was fairly obvious why to me. So in the days that followed I set out to keep the original spirit of the game but fix it so that it worked. Of course the moment I started doing so I went off on a tangent and made another game instead. But afterwards I went back and made the original game, so it was all good :p
Both games use the original hex shaped board divided into triangles. So I went out in search of a Kent set* to make a board and pieces. Apparently they aren't being made anymore, and no other company has stepped in to fill the breach. Long story short, I bought a crappy geometry set from Coles for 50c, and then the next day went to a newsagent and shelled out $2.50 for a protractor that you can actually see through. Being able to see through your protractor is much more important than you would think for making precise angles. Anyway, turns out that I didn't need one anyway. Remember all those geometry/sketching tricks they drummed into us at high school? Turns out that they're actually pretty useful, assuming that at some point in your life you feel the hankering to draw giant hexagons, equilateral triangles and then subdivide those triangles a la Pascal's Triangle. You can make all of the above using nothing but string, compass, ruler and pencil, and it's actually pretty cool. It's especially cool if you're like me, and are so uncoordinated that cutting a straight line is difficult even when following a line drawn on the page , because all these methods are fairly idiot-proof.
*Kent sets were these geometry sets that everyone had in high school. They were fairly uber, packing clear plastic ruler, triangle ruler thingies and protractor, metal compass, and small but serviceable pencil
1. Drawing a hexagon using nothing but string, pencil, and a few miscellaneous items.
Decide where you want the centre of the hexagon to be and attach one end of the string there, using glue or a pin or whatever. Then make a loop on the other end and put this around the pencil. Draw a pretty circle**. Now position the part of the string that was at the centre to a point on the circumference of the circle and draw an arc with the string/pencil combination so that it cuts the circle twice. Then move the string to the point where you cut the circle with the arc and repeat. When you've reached the point where you first started just use a ruler to join the places where the circle was cut by the arcs and you'll end up with a hexagon.
**This is harder than it sounds, for me at least. It's quite difficult to keep the pencil at the same angle and thus keep the radius of the circle consistent.
Also, the reason I was using string instead of a compass in the first place was because the compass only lets you make circles of about 15cm radius at most, and I needed something.. bigger
2. Drawing equilateral triangles
Decide what side length you want the triangle to be, and then draw a line of that length using the ruler. Make the compass the same length of that line and position the point at one end of the line. Draw an arc upwards. Then place the point at the other end of the line and repeat. The place where the two arcs intersect is the last point of the triangle. Join the dots.
3. Subdividing equilateral triangles a la Pascal, aka bisecting a line.
Change the compass length to more than half the length of the line you want to bisect. Place the tip at one end of the line and draw an arc above and below the line. Then place the tip at the other end of the line and repeat. Now you should have two points where the arcs intersect with eachother. Place a ruler so that it's in line with these two points and where the ruler touches the original line is the halfway point of the line. Alternatively, draw the line to join the intersecting arcs and you'll have bisected the line at right angles
To subdivide a triangle, bisect each line and then join the 3 resulting points up to form four smaller triangles.
And thus ends the geometry lesson for today :p
I'll post more about the games at a later date when I have more to show off about them. Also, despite all my gloating about noob-friendly methods of drawing all these shapes they're still not perfect. When I drew the three main lines to break the hexagon into six triangles they didn't *quite* intersect nicely. Instead there's this tiny triangle of about one or two millimetre sides in the centre. It might not sound like much but it does bug me that I spent so many hours working on this stupid thing, and not have a better result.
Both games use the original hex shaped board divided into triangles. So I went out in search of a Kent set* to make a board and pieces. Apparently they aren't being made anymore, and no other company has stepped in to fill the breach. Long story short, I bought a crappy geometry set from Coles for 50c, and then the next day went to a newsagent and shelled out $2.50 for a protractor that you can actually see through. Being able to see through your protractor is much more important than you would think for making precise angles. Anyway, turns out that I didn't need one anyway. Remember all those geometry/sketching tricks they drummed into us at high school? Turns out that they're actually pretty useful, assuming that at some point in your life you feel the hankering to draw giant hexagons, equilateral triangles and then subdivide those triangles a la Pascal's Triangle. You can make all of the above using nothing but string, compass, ruler and pencil, and it's actually pretty cool. It's especially cool if you're like me, and are so uncoordinated that cutting a straight line is difficult even when following a line drawn on the page , because all these methods are fairly idiot-proof.
*Kent sets were these geometry sets that everyone had in high school. They were fairly uber, packing clear plastic ruler, triangle ruler thingies and protractor, metal compass, and small but serviceable pencil
1. Drawing a hexagon using nothing but string, pencil, and a few miscellaneous items.
Decide where you want the centre of the hexagon to be and attach one end of the string there, using glue or a pin or whatever. Then make a loop on the other end and put this around the pencil. Draw a pretty circle**. Now position the part of the string that was at the centre to a point on the circumference of the circle and draw an arc with the string/pencil combination so that it cuts the circle twice. Then move the string to the point where you cut the circle with the arc and repeat. When you've reached the point where you first started just use a ruler to join the places where the circle was cut by the arcs and you'll end up with a hexagon.
**This is harder than it sounds, for me at least. It's quite difficult to keep the pencil at the same angle and thus keep the radius of the circle consistent.
Also, the reason I was using string instead of a compass in the first place was because the compass only lets you make circles of about 15cm radius at most, and I needed something.. bigger
2. Drawing equilateral triangles
Decide what side length you want the triangle to be, and then draw a line of that length using the ruler. Make the compass the same length of that line and position the point at one end of the line. Draw an arc upwards. Then place the point at the other end of the line and repeat. The place where the two arcs intersect is the last point of the triangle. Join the dots.
3. Subdividing equilateral triangles a la Pascal, aka bisecting a line.
Change the compass length to more than half the length of the line you want to bisect. Place the tip at one end of the line and draw an arc above and below the line. Then place the tip at the other end of the line and repeat. Now you should have two points where the arcs intersect with eachother. Place a ruler so that it's in line with these two points and where the ruler touches the original line is the halfway point of the line. Alternatively, draw the line to join the intersecting arcs and you'll have bisected the line at right angles
To subdivide a triangle, bisect each line and then join the 3 resulting points up to form four smaller triangles.
And thus ends the geometry lesson for today :p
I'll post more about the games at a later date when I have more to show off about them. Also, despite all my gloating about noob-friendly methods of drawing all these shapes they're still not perfect. When I drew the three main lines to break the hexagon into six triangles they didn't *quite* intersect nicely. Instead there's this tiny triangle of about one or two millimetre sides in the centre. It might not sound like much but it does bug me that I spent so many hours working on this stupid thing, and not have a better result.
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I think I was looking at this and Riemann on precisely this same day