We all probably seen a circle built in Minecraft, on a Youtube video or on a server - probably even tried ( and possible succeeded) to build one. But what is so good about a circle in Minecraft?

Advantages of Circles

For this I will list the advantages and give a brief example/explanation.

- Circles in Minecraft are something different due to the games voxel/cubic nature, making circles somewhat more complex to grasp and more unique.
- Circles can be coupled with rectangular shapes to create interesting designs and architectures because makes it geometry of these designs are more complex. For example check my warp /warp ArchetypeOpus
- There is a greater variety of designs you can do because you can build as many as you can imagine of circular designs and designs of the combination of the two, as well as rectangular designs.
- In survival, or in any gamemode, it is easier to light cylindrical buildings as there are no dark corners to light.
- If you building in a jungle or forest or anywhere that needs clearing, it takes less time clearing cylindrical areas to make space for circular designs than clearing rectangular areas for rectangular designs, because circles take up less area than rectangles.
- Corners are sharp.

Building Circles via a Circle Sheet

There are many images on Google Images or similar of Minecraft Circle Diagrams so obtaining one shouldn't be too hard. Using circle sheets is the simplest method to work with as you only need to copy the diagram's instructions. However, it may be a bit frustrating switching between Minecraft and the circle sheet if you can't see both at one time. The results are really dependant on how the author obtained these circles for his circle sheet. So the accuracy of a circle sheet to a actual pixel representation of a circle varies.

Simplicity of the Method: Simplest.

Level of Frustration from this Method: Frustrating.

Accuracy of the Method to the actual pixel representation of a circle: Varies.

Building Circles by sight/guess

This requires no real presentation or working out for this one, just a few steps.

- Plan out a cross, with blocks, with each beam being the length of the radius.
- Extend two lengths of little less than third of the radius (A third of the radius if the radius is small) of blocks either side of each beam.
- Moving one inwards and across add another length of blocks but one less block than the last length.
- Repeat this step until they meet up at one block's length, you may have to remove more than one block on that step for the ends to meet like that.
- Remove the cross and tidy the circle to eye if needed.

This method isn't too simple and if you have OCD then you will be sent mad by the inaccurate results produced from this method, yet if it doesn't bother you then it isn't an annoying method. The results as mentioned before varies but it usually ends up inaccurate to the actual pixel representation of a circle.

Simplicity of the Method: Not too simple.

Level of Frustration from this Method: Ok, for the results you get and if you remember the steps.

Accuracy of the Method to the actual pixel representation of a circle: Usually inaccurate.

Building Circles using the Cartesian Equation of Circles

This is the hardest method and yet produces the most accurate results as it is the actual pixel representation of a circle depending on how you round values.

You must have decent knowledge of algebra; be able to rearrange and substitute values into pythagoras equations; understand the Cartesian Coordinate System, which is just your basic coordinates system like (3,4); and identify operators on a pc and calculators and use them on a calculator e.g. Multiply is: *, Divide is: /, Power of 2 is: ^2, and Square Root is: ^0.5. It will be difficult to root values in your head, so have a calculator ready.

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`This is the equation of a circle: (x-a)^2 + (y-b)^2 = r^2 ( A glorified pythagoras equation.)`

Where r is the radius, (a,b) is the centre of the circle.

In this case the centre will be at (0,0), so the equation now looks like: x^2 + y^2 = r^2

We then substitute whole values from -r to r into x, maybe prepare a table of values for two y values.

Rearrange the equation so that y^2 is the subject: y^2 = r^2 - x^2

Square root the equation so that we only get y as our subject: y = (r^2 - x^2)^0.5

Calculate your answers. For this you will get two values of y: positive (r^2 - x^2)^0.5 and negative (r^2 - x^2)^0.5.

Round the y values to the nearest whole number.

If you have a table of values, record all the y values you calculated.

Then using the centre of where your circle will be, plot out your circle using all x values and all y values.

Fill in any gaps in the circle to make it look symmetrical.

You have a circle that is about a circle as you can get it in Minecraft.

If you don't get it don't worry about it.

This, like said before, is the hardest method and probably torture for some - yet the results are the most accurate.

Simplicity of the Method: Very difficult if you're not up to check with the list of requirements.

Level of Frustration from this Method: Torture for those who don't fully get it.

Accuracy of the Method to the actual pixel representation of a circle: Most accurate.

Note: This topic is not fully finished. Images will be added soon! And this will probably help visualize.