A joke that needs to be explained, isn’t a good joke.

But in this case, there is a huge exception. Because, you might loose your fear of math.

If not, you at least learn something about two of the most feared symbols in math.

Σ (sigma) and ∫  (script)

The meme in question?

This meme is quite clever

It compares two potato-peeling methods to two mathematical concepts from calculus.

On one side, there's "Me peeling potatoes,". This symbolizes a more basic approach - think of peeling potatoes by cutting away a lot of the actual potato with the skin, getting rough edges. Fast and easy.

Then, there's "my mum peeling potatoes,". Smooth surface, no edges. Just the skin was removed. This suggests a seamless, more adept technique, like a seasoned chef's skill.

The joke's essence?

It is using mathematical concepts as a metaphor for the quality of potato peeling.

How I peel potatoes

The "me" part, indicating a choppy, less precise peeling method, with visible flat segments or "steps" on the potato surface is essentially displaying the Riemann sum.

A Riemann sum is a method for approximating the area underneath a curve on a graph.

In this graph, you can see the the Riemann sum approximation in action for the area from x=3 to x=5 with 10 rectangles. The area is basically split into 10 rectangles with the height of the graph at this point.

Because rectangles are easy to calculate, right?

And all rectangles areas get add up to get a rough value for the surface area of the graph between 3 and 5.

You can clearly see the “steps”.

And this is basically what Σ means

Step by step calculate the function beside the sigma. And do this for n times. The function is multiplied by the width of a section in each step. Sum up all the results. Done!

Back to my mum…

What about “my mums” potato peeling skills…

The "my mum" part implies a smooth, more professional approach, resulting in a potato that has a very smooth surface, much like a continuous curve, here represented by another mathematical approach. The integral.

While a Riemann sum uses a finite number of rectangles with finite width, an integral uses an infinite number of infinitesimally thin rectangles to perfectly capture the area under the curve.

Lets look at a Riemann sum again, this time with 50 rectangles. Pretty close to the curve, right?

Now, lets make the rectangles the smallest we can. Infinititisimally small as we call this in math.

And this is the closest we can get to the curve. The limit of Riemann sums with an ever increasing number of rectangles, ultimately becoming so many and so small, they become a continuous area.

That’s what the ∫ actually means

Like the numbers below and above the sigma the integral symbol also has limits of integration. And there is also a function that is calculated with a changing value.

This time however, the steps are a component (dx) that defines the infinitesimal small change of x in each step until x reaches the upper limit. And all this calculated function results are yet again summed up. In a more continuous way, though.

Yeah, but how is all this used in real life?

Integrals are used to determine the total force acting on a gear tooth by integrating the pressure distribution over the contact area. This helps engineers assess the load-carrying capacity of the gear.

Integrals are indispensable in electrical engineering for analyzing circuits. They enable engineers to calculate the total charge passing through components, which is vital for energy and power calculations.

And here we are again.

What a journey. From peeling potatoes the “right” way, to gears in clinch…

So long

Sebastian