Minecraft may seem like your standard game, but it is much deeper than it appears. This iteration of MathCraft Is all about linear equations and their uses in Minecraft. Many of you may already know about these, or maybe you don’t quite know what they are. Either way, you will hopefully learn how to make your next build even better.
First, let’s look at the linear equations formula.
y=ax+b
“Y” is equal to the height of the block. “A” is equal to the slope of our line. “X” is the distance horizontally from the start of a line to the block you are placing. “B” is the starting height.
This equation can be used to do all sorts of things that involve lines. Imagine you want to make a slanted wall or roof. You know how far it needs to go, and you also know the top and bottom. Using that information, you can create an equation to make your life easier, and remove any guessing. For this example we want a roof that starts 40 blocks high, goes for 30 blocks, and ends 20 blocks high. Using this information, you can create an equation. Now we need to make a data table to organize what we have.
| start | end | |
| horizontal | 0 | 30 |
| vertical | 40 | 20 |
Time to put this data into the equation from above.
1. Subtract the ending height (20 in this example) by the starting height (40 in this example). You should get -20 for this part.
2. Divide that number (-20 in this example) by the total distance (30 in this example). You will get -.66 repeating. Let’s make that a fraction and say -2/3. This is your slope or “A” value from the equation above.
3. Take your starting value (40 in this example) and make that the starting height or “B” value from the equation above.
Now, there is an equation to map the placement of blocks.
Y=-2/3 * x + 40
Finally, we use this equation to map out where blocks go. To do this, replace the “X” with whole numbers up to the length (30). You will get decimals so just round to the nearest who number. Whatever you get for “Y” is the height of the block to place. If you have been following this example, you should get something like this:
This is what you should get if you have been following the linear equations tutorial. A sign is placed every 5 blocks.
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