Hi and welcome to the forum. Below is the response I received along with the image representation. Without some iterative adjustment, Dall-E is going to struggle with a visual representation of the precise layout of the yoga mats. However, you can see by the detailed explanation that it gave, that you should be able to fit 63 mats in the space utilizing 3 sets of concentric circles. Hope this helps!
First, let’s verify the calculations:
The standard size of a yoga mat is approximately 24 inches (0.6 meters) wide and 72 inches (1.8 meters) long.
The diameter of your meditation area is 8 meters, so its circumference is π×diameter=π×8π×diameter=π×8 meters or approximately 25.13 meters (988.976 inches).
You want to leave at least 30 cm (about 12 inches) around each mat.
Now, let’s calculate how many mats can fit around the circumference of the circle:
The width of each mat plus the required space around it is 24 inches+12 inches=36 inches24 inches+12 inches=36 inches.
Dividing the total circumference by this combined width will give us the number of mats that can fit around the circle.
Next, we need to consider the inner circles. As the mats are laid out in concentric circles, each inner circle’s circumference will be smaller, and thus it will fit fewer mats.
I will perform these calculations to determine the accurate number of mats for both the outer and inner circles. Let’s start with the outer circle.
The calculation for the outer circle aligns with your estimate: approximately 27 mats can fit around the circumference of an 8-meter diameter circle, accounting for the size of each mat and the required space around them.
Now, for the inner circles, the process involves calculating the circumference of each smaller circle and then determining how many mats can fit in each of these circles. The number of inner circles and the number of mats in each will depend on the remaining space after accommodating the outer circle.
Let’s proceed with these calculations.
Based on these calculations:
The first inner circle can accommodate approximately 21 yoga mats.
The second inner circle can accommodate approximately 15 yoga mats.
So, in total, we have 27 mats on the outer circle, 21 on the first inner circle, and 15 on the second inner circle. This gives us a total of 63 mats.
Now, let’s create a visual representation based on this layout.