Recently i started playing a lot of Minecraft and i really want to get better at building. I want to learn how to build towers but for that i need to build circle structures. I searched up on Youtube some Tutorials but i could only find tutorials on how to do that with command blocks and circle generator websites. Im in survival mode in my world and i don't really wanna cheat by using command blocks or special websites as i consider that kind of cheating and i wouldn't learn anything. Anyone has any tips for me to improve making circle structures in Minecraft? (Also, sorry for bad english im from italy lol)

Recently i started playing a lot of Minecraft and i really want to get better at building. I want to learn how to build towers but for that i need to build circle structures. I searched up on Youtube some Tutorials but i could only find tutorials on how to do that with command blocks and circle generator websites. Im in survival mode in my world and i don't really wanna cheat by using command blocks or special websites as i consider that kind of cheating and i wouldn't learn anything. Anyone has any tips for me to improve making circle structures in Minecraft? (Also, sorry for bad english im from italy lol)

When building circular structures, what I like to do first is to create an outline of the circle, which will tell you roughly how large it should be. The key to building circles is symmetrically. In real life, a circle has infinite lines of symmetry, but this is not possible in Minecraft, so the aim is to have as many lines of symmetry as possible, depending on the size of the circle. For the smallest circles, which are essentially squares but without the corners, four is a good starting point. For larger circles, simply increase the length of the four perpendicular sides and add more diagonals in between. Here are some circle models that should help if you are still confused.

The math to make your own circle generator or make circles using mental math. This is going to assume you're familiar with geometry and algebra at a high school level. This is based on Bresenham's circle method, though simplified a lot.

First, if you've built a circle before, you've probably realized that it has 8-fold symmetry like this--once you make 1/8th of the circle, you can copy that pattern 7 more times to finish the circle. (In the diagram, the solid red/blue bit is all we need to calculate, and the rest is just repeating that. The 8 blue pixels are all the same point in the pattern, just in different rotations.)

Now, in math you learn that this equation defines the points within a circle:

If we set this to r=5, and then compute every block that satisfies this, we get this kinda weird spiky circle (left):

This left one does have a radius of 5, since the furthest points are 5 blocks from the center. But it doesn't look great. The point (5, 0) has x^2 + y^2 = (25) + (0) <= 25, but (5, 1) doesn't fit. So only the points exactly on the x/y axes directions actually have the radius of 5. Minecraft circles (usually, but not always) look best when the cardinal-direction edges are the longest flat surfaces, like the circle on the left. To do that, we modify our circle equation to be "the biggest circle that doesn't have a radius of 6 along the cardinal directions"

(A variant of this is "the biggest circle that's closer to radius 5 than radius 6. I think this is more commonly used by "circle generator" sites, but it makes the math a bit more complicated.)

Now, here's where you get your graph paper, a spreadsheet, or something similar. Let's make a circle of radius 6, so 13 blocks in diameter. (6+1)^2 = 49, so a block is part of our circle if its X and Y coordinates squared sum to less than 49. (If we wanna use the (r + 0.5), we can, and then the number to compare against is 42.25.) Our starting point is obviously going to be (6, 0), since 7^2 is too big. The next question is, is (6, 1) part of our circle? The squares sum to 36+1=37, so it is! So we move up one more square and keep checking.

Then we hit (6, 4). Uh oh, the sum of its squares is 52, and 52 > 49! So that's not part of our circle, we mark it with an x.

So we need to move inwards 1 block on the x direction to find something with y=4. So we check (5, 4). Its sum of squares is 41, which fits, and then (5, 5) is 50, which doesn't fit.

We hit the diagonal y=x line! Since we remember that we only need 1/8th of the circle, we're done! Color in the squares we drew checks in, then reflect them to complete the circle.

That's the step-by-step pencil-and-paper method. Once you get used to it, the problem becomes: Choose an r^2. Then for x < r, solve for y such that y^2 < (r^2 - x^2).

So for a r=11 circle: (r+1)^2 = 144 is our criteria. Starting at x = 11, x^2 = 121, 144-121=23, 4^2 is the largest square less than 23. So fill in (11, 0) through (11, 4) and then move onto x=10, 144 - (10^2) = 44, the largest square there is 6^2. So we fill in (10, 5) and (10, 6). Then go onto x=9...

Hope that makes sense! And once you understand the math, it's not cheating to use a calculator to do it for you.

Recently i started playing a lot of Minecraft and i really want to get better at building. I want to learn how to build towers but for that i need to build circle structures. I searched up on Youtube some Tutorials but i could only find tutorials on how to do that with command blocks and circle generator websites. Im in survival mode in my world and i don't really wanna cheat by using command blocks or special websites as i consider that kind of cheating and i wouldn't learn anything. Anyone has any tips for me to improve making circle structures in Minecraft? (Also, sorry for bad english im from italy lol)

When building circular structures, what I like to do first is to create an outline of the circle, which will tell you roughly how large it should be. The key to building circles is symmetrically. In real life, a circle has infinite lines of symmetry, but this is not possible in Minecraft, so the aim is to have as many lines of symmetry as possible, depending on the size of the circle. For the smallest circles, which are essentially squares but without the corners, four is a good starting point. For larger circles, simply increase the length of the four perpendicular sides and add more diagonals in between. Here are some circle models that should help if you are still confused.

The math to make your own circle generator or make circles using mental math. This is going to assume you're familiar with geometry and algebra at a high school level. This is based on Bresenham's circle method, though simplified a lot.

First, if you've built a circle before, you've probably realized that it has 8-fold symmetry like this--once you make 1/8th of the circle, you can copy that pattern 7 more times to finish the circle. (In the diagram, the solid red/blue bit is all we need to calculate, and the rest is just repeating that. The 8 blue pixels are all the same point in the pattern, just in different rotations.)

Now, in math you learn that this equation defines the points within a circle:

If we set this to r=5, and then compute every block that satisfies this, we get this kinda weird spiky circle (left):

(Circles by mccirclegenerator)

This left one

doeshave a radius of 5, since the furthest points are 5 blocks from the center. But it doesn't look great. The point (5, 0) has x^2 + y^2 = (25) + (0) <= 25, but (5, 1) doesn't fit. So only the pointsexactlyon the x/y axes directions actually have the radius of 5. Minecraft circles (usually, but not always) look best when the cardinal-direction edges are the longest flat surfaces, like the circle on the left. To do that, we modify our circle equation to be "the biggest circle that doesn't have a radius of 6 along the cardinal directions"(A variant of this is "the biggest circle that's closer to radius 5 than radius 6. I think this is more commonly used by "circle generator" sites, but it makes the math a bit more complicated.)

Now, here's where you get your graph paper, a spreadsheet, or something similar. Let's make a circle of radius 6, so 13 blocks in diameter. (6+1)^2 = 49, so a block is part of our circle if its X and Y coordinates squared sum to less than 49. (If we wanna use the (r + 0.5), we can, and then the number to compare against is 42.25.) Our starting point is obviously going to be (6, 0), since 7^2 is too big. The next question is, is (6, 1) part of our circle? The squares sum to 36+1=37, so it is! So we move up one more square and keep checking.

Then we hit (6, 4). Uh oh, the sum of its squares is 52, and 52 > 49! So that's not part of our circle, we mark it with an x.

So we need to move inwards 1 block on the x direction to find something with y=4. So we check (5, 4). Its sum of squares is 41, which fits, and then (5, 5) is 50, which doesn't fit.

We hit the diagonal y=x line! Since we remember that we only need 1/8th of the circle, we're done! Color in the squares we drew checks in, then reflect them to complete the circle.

That's the step-by-step pencil-and-paper method. Once you get used to it, the problem becomes: Choose an r^2. Then for x < r, solve for y such that y^2 < (r^2 - x^2).

So for a r=11 circle: (r+1)^2 = 144 is our criteria. Starting at x = 11, x^2 = 121, 144-121=23, 4^2 is the largest square less than 23. So fill in (11, 0) through (11, 4) and then move onto x=10, 144 - (10^2) = 44, the largest square there is 6^2. So we fill in (10, 5) and (10, 6). Then go onto x=9...

Hope that makes sense! And once you understand the math, it's not cheating to use a calculator to do it for you.

Thank you! You really helped a lot