Queen Marika's Essays / No. 116: Why the Area Changes

Hello 😀✨ I'm Marika ⭐️
Today, I am posting an extra edition of my essays.


This is because a conversation in the comments section of the previous post (No. 115) expanded, and I have something I should share.


I have changed my plans and will post the side story of General Houseki V, which I was scheduled to post today, tomorrow instead. 🙇‍♀️

No. 116: Why the Area Changes

The previous post was about, "Why does the area change depending on how you enclose it, even with a ribbon of the same length?"

It's a story like this.

So~.
I received many comments, so I will explain the answer while introducing them 😆

Part 1

This is the content that I thought was "almost the answer."Macchan-san It arose from an exchange of comments with.

The perimeter is addition, but the area is multiplication.

That's the story.

Make a 20 cm ribbon into a square with sides of 5 cm.
In this case, the sum of the length and width is 5 + 5 = 10.
But if you multiply the length and width (area), it is 5 × 5 = 25.

Make a 20 cm ribbon into a rectangle with a length of 6 cm and a width of 4 cm.
In this case, the sum of the length and width is 6 + 4 = 10.
But if you multiply the length and width (area), it is 6 × 4 = 24.

In short, even with combinations of numbers where the answer to addition is the same, the value becomes different when multiplied.
Is that the only reason why the perimeter and area of a shape don't match?
Whether it's a valid reason or not, that's what the discussion is coming down to.

Part 2

The person who gave me the comment isGuko-san.
It feels like a solution to a proof problem on a high school entrance exam, but it is expressed well.

Take a square with a side of a cm, extend its length by b cm, and shorten its width by b cm.

The fact that the area changes is expressed mathematically.

Even though the amount extended and the amount shortened are the same, the area changes because it is multiplication.

Multiplying the extended amount (a positive number) by the shortened amount (a negative number) results in a negative number. That is the mechanism.

For quadrilaterals with the same perimeter, the square has the largest area.

I was thinking about this, and... 😅
Ultraman Tiga changes his form by adjusting the balance between power and speed, but the setting is that the Multi Type, which has a stable balance of power and speed, is the strongest.

I thought this image fits perfectly... what do you think?

The reason this thought crossed my mind is because Kanon Yoshioka commented, "Couldn't this be a topic for creative work?" so I introduced it as an example that might have already been utilized 😅

Saki-san also gave a similar comment 😌

Akane-san expressed the change in area with a diagram ⭐️

I think it's amazing that she created this diagram in such a short time, and I think it's a good explanation for elementary school students, so if you are interested, please check the link 😆

Shiawase to Kenko-san also wrote an article about this matter.
If you are interested in this as well, please check the link 😆

That concludes this extra edition, No. 116!
If you have any further opinions, please let me know in the comments section 🙇‍♀️

Click here for other articles in the Essays series!