A perfect square inside a circle and a perfect square

In summary, the conversation discusses the relationship between a perfect square inscribed inside a circle and a perfect square circumscribing the circle. The question is whether the extra bits between the inner square and the circle are equal to the extra bits between the circle and the outer square. The conversation leads to finding the areas of the objects in order to answer the question.
  • #1
gonnis
7
0
A perfect square inside a circle (so the inner square's corners touch the circle) and a perfect square surrounds the circle (so the circle touches the sides of the outer square. Are the extra bits between the inner square and the circle equal to the extra bits between the circle and the outer square?
Im not explaining this very good but hopefully the question makes sense. Don't know how to include a drawing here.
Thanks
 
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  • #2
This looks like a homework question, if so it belongs in another forum I think.
Anyway, do you know the area of a square?
Do you know the area of a circle?
 
  • #3
No barefeet this isn't a homework problem lol... its just been a while since I've thought about circles... I am asking in the context of before pi. OK its grade school question, its sort of stupid, but its legit, please indulge if you don't mind.
(fyi I asked a similarly dull question in gen discussion and they moved it to gen math, so I figured I may as well just post here because it would probably get moved lol)
thanks!
 
  • #4
gonnis, why would you think the area between the inner square and the circle would be equal to the area between the circle and the outer square? Have you made an attempt to come up with an answer for yourself?
1. Start with a unit circle centered at the origin. Its equation is x2 + y2 = 1.
2. Inscribe a square inside the circle, then find the coordinates of the corners of the inner square.
3.Circumscribe a larger square around the circle, and find its corner points.
4. From the information obtained, you should be able to find the areas of all of the objects here, and thereby answer your question.

(BTW, "perfect square" is redundant - a square is a square.)
 
  • #5


I can say that the answer to this question depends on the specific measurements and proportions of the shapes in question. In general, the extra bits between the inner square and the circle may not be equal to the extra bits between the circle and the outer square. This is because the size and placement of the shapes can vary, resulting in different amounts of space between them.

However, if we assume that the inner square and the circle are both perfect squares with the same side length, and the outer square is also a perfect square with a side length that is twice the length of the inner square, then the extra bits between the inner square and the circle would be equal to the extra bits between the circle and the outer square. This is because the proportions of the shapes would be the same and the extra bits would be evenly distributed.

In general, it is important to carefully consider the measurements and proportions of the shapes in question before making any assumptions about the equality of the extra bits. In some cases, they may be equal, but in others, they may not be. This is something that can be explored further through mathematical calculations and visual representations.
 

1. What is a perfect square inside a circle and a perfect square?

A perfect square inside a circle and a perfect square refers to a geometric shape where a square is inscribed inside a circle, and another square is circumscribed around the same circle.

2. What are the properties of a perfect square inside a circle and a perfect square?

The properties of a perfect square inside a circle and a perfect square include: the square's corners touching the circle, the square's sides being tangential to the circle, and the square's diagonal being the diameter of the circle.

3. How are the areas of the two squares related in a perfect square inside a circle and a perfect square?

The area of the inscribed square is half the area of the circumscribed square. In other words, the area of the inscribed square is equal to the area of the circle multiplied by 0.5, or half its area.

4. What is the ratio of the side lengths of the two squares in a perfect square inside a circle and a perfect square?

The ratio of the side lengths of the inscribed and circumscribed squares is equal to the square root of 2, or approximately 1.414. This means that the diagonal of the inscribed square is equal to the side length of the circumscribed square.

5. How is a perfect square inside a circle and a perfect square used in real life?

A perfect square inside a circle and a perfect square has various applications in mathematics and engineering, such as constructing tangents, calculating the area of a circle, and designing circular structures like bridges and buildings.

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