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- เผยแพร่เมื่อ 22 ก.ย. 2024
- Can you work out the area of the quarter circle? How did you find it? Watch the video to see my solution! Was your solution different to mine? Let me know in the comments below!
This is a problem shared on twitter by: x.com/sonukg4i...
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The question really needs to specify that those are a quarter-circle and a quarter-ellipse. You really can't just eyeball what a curve is.
Hi, I specified at the start of the video that there were 4 rights angles at the centre of the shape and therefore the bottom left and top right shapes must be a quarter circle and ellipse respectively. I show in the video that it is a quarter ellipse by drawing the full ellipse. I didn't do the same for the quarter circle as I didn't feel it was necessary.
Hope you enjoyed the video regardless :)
@@mrtalbotmaths I assumed the top right part is a horizontal half parabola, which contradicts the horizontal tangent (not specified in the question, though). If we assume a horizontal tangent, it could have been almost any curve with equation (x/c)^r + (y/b)^r = 1. The same is true about the bottom-left shape. Specify these things in your declaration of the problem!
The right angle is necessary but not sufficient to prove that the bottom left shape is a quarter circle. This could be any other curve (including a non-circle ellipse) so we cannot conclusively prove it is a quarter circle.
I've updated the thumbnail now to clarify, sorry about any confusion. Hope you liked the video/problem nonetheless!
That's not a quarter circle, you just assume it is. You have to do it assuming it's a quarter ellipse
Hi, I specified at the start of the video that there were 4 rights angles at the centre of the shape and therefore the bottom left and top right shapes must be a quarter circle and ellipse respectively. I show in the video that it is a quarter ellipse by drawing the full ellipse. I didn’t do the same for the quarter circle as I didn’t feel it was necessary. Hope you enjoyed the video regardless :)
@@mrtalbotmaths That doesn't follow. Just stretch the whole shape vertically and you still have right angles at the centre but you no longer have a quarter circle. And drawing an ellipse and showing it lines up isn't really a mathematical proof.
You can easily have a shape that looks like a circle or an ellipse but isn't. In a maths problem, you should never assume that just because something looks like a particular shape it is that shape. If it isn't specified in the question and you can't prove it from information that is specified in the question, you can't assume it. In this case, there isn't enough information provided to answer the question.
I've updated the thumbnail now to clarify, sorry about any confusion. Hope you liked the video/problem nonetheless!