Mowing your lawn with a mower is the task you perform regularly to keep your lawn in a good looking state. Have you ever thought of mowing your lawn using calculations? We have come up with some mathematical calculations that can surely help you in lawn mowing.

## Mowing your lawn using Math

In the school and college years, we all must have applied math in solving different problems. But, now we will apply math in solving the lawn mowing problems. There are two types of lawn; one is simple lawns, and the other is weird type lawns.

### Mowing Pattern

Some people mow their lawn like they go to the end and make a 180-degree turn and come back to the other way and again repeat this mowing pattern. This pattern takes more time and effort because by adopting this way people are moving very slowly and it is like maneuvering the mower around.

Another way of mowing is in a spiral pattern rather than back and forth movement. In this pattern, you move to the end, make a right turn, go to the other end again, then go back to the end, and repeat until you finish mowing your lawn. This pattern is less time consuming because every time you take full iteration around, you will be one mower width less wide.

Now we will explain the theories behind this quick mowing pattern:-

- Each rotation takes one less width similar to the mower’s width.
- Each turn will take less time as compared to the previous turn.

To graph these theories you will need graph paper, and draw a couple of lots on it. Let’s assume that the lot that you are mowing is 10m×10m, and each square is 1m. So, you need to draw a vertical line on the graph by counting to 10 boxes, and a horizontal line by counting to 10 boxes. Then make a square by joining these lines altogether. Now suppose that your mower deck is 1m×1m square.

### Math and Geometry

We will assume that math and geometry for this lawn mowing are the same regardless of any dimensions as long as we are dealing with the squares, and we cover every strip at 1m per second.

Mower deck = 1^{2 }

Mow velocity = 1m/second

We will compare the number of turns to the number of turns with the amount of time each turn takes in the 180 degrees type pattern of mowing. We will assume this number as 6.

180° = 4 seconds

90° = 2 seconds

These assumptions will hold up for figuring out what we are doing. So, let’s calculate how long it takes for a normal average homeowner to mow a lawn area of 10m×10m with a one-meter mower.

Make 9 strips on the graph paper in the square that you have already made. We will be able to calculate that it will take 10 seconds to mow a 10m area, and then you will take a turn and again will take 10 seconds to come back.

10m×10m = 100 (seconds)

Also, add up the time you will take for turning. There is a total of 9 turns and every 180 degrees turn will take 4 seconds. So,

9×4 = 36 (seconds)

Now,

100 sec + 36 sec = **136 (seconds)**

Therefore, it will take 136 seconds to mow your lawn in 180-degrees turning around the pattern.

### Spiral Pattern

We will also calculate the mowing of the lawn according to the spiral pattern.

We will apply basic math on it, and the amount of time it takes to mow 10m×10m at the rate of 1m per second. The amount of time it takes to mow should be 100 seconds like before. Just to see if this math is correct or not we will add up all the sections of the pattern and after calculating through the calculator we will get 90.

Therefore, it is the same amount that we got for the first pattern. Now, we will calculate several turns in this pattern. The total number of turns is 18, and every turn is a 90-degree turn. 90 degrees turn will take 2 seconds as we have already calculated this.

So,

18 × 2 = (36 seconds)

If we add several sections in it we will get,

90 + 36 = **126 (seconds)**

In the end, you have seen that the time for mowing your lawn has become less if you mow it in a spiral pattern and there is a difference of 10 seconds when we compared the time taken for both patterns.

From the above calculations about mowing your lawn, we will be able to understand and adopt the better techniques of trimming the lawn grass with less time and better measurements. Always remember that every lawn has its size and shape, so you apply math according to your area/property, it was just a general and assumed idea that we have explained to help you.** **