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Is the the most baffling geometry question ever posed for a 7 year old pupil?
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Feb 27, 2021 21:23:30   #
jayluber Loc: Phoenix, AZ
 
Seems like a great question for 80+ year olds sitting home with nothing better to do.
IMHO...

Feb 27, 2021 21:30:11   #
robertjerl Loc: Corona, California
 
jayluber wrote:
Just asking - what's the Tangent of a 0 deg angle? the intersection of the semicircle with the base line? I think it's zero degrees. SOH CAH TOA ..Opposite over the adjacent. Therefore, the arc intersects the straight line at a 90 deg angle.
Who needs to be fired???


It intersects at 90°-well almost-and only at one single point. A right angle is one that a square can be fitted to the inside for a perfect fit. And if you tried that here no matter how small you made the square if you enlarge enough you find that it doesn't fit because one of the lines is a curve. It takes two straight lines to make a right angle and there is only one straight line here. The other is a curve

I see it more as a thinking problem than a geometry or math problem. You have to answer by thinking about what a right angle is, not visual impression.

This of course is only if the person who created the problem doesn't count the frame as part of the figure and then the answer is still false because it clearly asks if there are two right angles, no other number - 2.

Feb 27, 2021 21:48:54   #
2Dragons Loc: The Back of Beyond
 
robertjerl wrote:
It intersects at 90°-well almost-and only at one single point. A right angle is one that a square can be fitted to the inside for a perfect fit. And if you tried that here no matter how small you made the square if you enlarge enough you find that it doesn't fit because one of the lines is a curve. It takes two straight lines to make a right angle and there is only one straight line here. The other is a curve

I see it more as a thinking problem than a geometry or math problem. You have to answer by thinking about what a right angle is, not visual impression.

This of course is only if the person who created the problem doesn't count the frame as part of the figure and then the answer is still false because it clearly asks if there are two right angles, no other number - 2.
It intersects at 90°-well almost-and only at one s... (show quote)


Ah, the voice of reason and logic!

 
 
Feb 27, 2021 23:50:16   #
Mike from Point
 
There are 2 right angles. But it soon turns to less than right agles.

Feb 28, 2021 02:59:05   #
oregonfrank Loc: Astoria, Oregon
 
Typical children at age 7 are learning counting, addition and subtraction, usually via concrete experiences. Multiplication and division are usually introduced at ages 8 and 9. Confronting young children with learning tasks they cannot understand and whose brains are not developed enough to embrace is not the best teaching technique! Abstract thinking skills are not usually present at age 7. Understanding the definition of a right angle involves also understanding that a complete circle consists of 360 degrees and that any angle of > or < than 90 degrees is not a right angle. Finding a 7 year old child who engages in this level of abstract thinking would be a rare find indeed. Perhaps the most intelligent of the top 1% whose parents are engineers!! Frank

Feb 28, 2021 03:02:16   #
TheShoe Loc: Lacey, WA
 
george19 wrote:


Yes, technically there are two right angles in the figure, but they are made by the instantaneous tangent at the intersections, developed from an infinitesimal delta there, i.e., calculus.

Nope. Using your infinitesimal deltas, you are immediately deviating from the tangent when you proceed away from the radius. Either that or you have found that a line is defined by a single point. Good luck with that one.

Feb 28, 2021 04:31:46   #
JADAV
 
On a semicircle the curve of the circle meets the end of the diameter at 90 degrees. Should the semicircle be at a scale say as large as the Earth, then someone standing at the end of the diameter wouldn't question that there was a right angle and would need an extremely accurate method of measurement to detect the curve. The question leads one to consider the situation from a different viewpoint and is an excellent teaching tool but I'm not sure that 7 year olds are generally ready to take it on board. I'm not surprised that a Professor has difficulty with this question as he has been trained to apply the language of mathematics to find an explanation that can be expressed in numbers. The Greeks had a similar problem with the concept of infinity when explaining a hare chasing and overtaking a tortoise. They calculated arithmetically that the distance between the two would get shorter and shorter but if this can be done repeatedly into infinity then the hare never actually catches the tortoise. Similarly I've seen mathematicians struggle with the following question: if a rope is stretched across the top of two posts (each 2 feet tall) that are 4 feet apart then how close together do the posts need to be moved towards each other for the rope to dip down and touch the ground? They have come up with all sorts of formulae to arrive at the answer whilst a non-mathematician will quickly tell you that the need to be moved together! Another way to "fox" a mathematician is to ask him "How far can a pack of hounds chase a fox into a wood?" the answer is "to the middle". Once the fox has passed the middle of the wood the hounds are chasing it out of the wood but of course this isn't easily expressed in a mathematical form.

 
 
Feb 28, 2021 06:50:14   #
Dannj
 
oregonfrank wrote:
Typical children at age 7 are learning counting, addition and subtraction, usually via concrete experiences. Multiplication and division are usually introduced at ages 8 and 9. Confronting young children with learning tasks they cannot understand and whose brains are not developed enough to embrace is not the best teaching technique! Abstract thinking skills are not usually present at age 7. Understanding the definition of a right angle involves also understanding that a complete circle consists of 360 degrees and that any angle of > or < than 90 degrees is not a right angle. Finding a 7 year old child who engages in this level of abstract thinking would be a rare find indeed. Perhaps the most intelligent of the top 1% whose parents are engineers!! Frank
Typical children at age 7 are learning counting, a... (show quote)


Children at 7 can recognize shapes without understanding their geometric components. You can show them a three sided figure and tell them it’s a triangle and they’ll remember it. You can also tell them that the corners of the triangle are called angles and they’ll remember that also but it’s purely a memory function, not understanding. It’s possible that you could draw a shape for a 7 year old and tell them it’s called “right angle”. Then show them a group of shapes and ask them to pick out the “right angle”. They may choose the correct one but again, it’s visual recognition not understanding.
That being said, a 7 year old with exceptional visual compression skills may look at the picture in the original post and “see” a right angle at the points where the line intersects with the curve. Again, it’s visual recognition not comprehension.
I’m not addressing whether the original picture does or does not contain a right angle...just how a 7 year old might see it.

Feb 28, 2021 14:33:54   #
TheShoe Loc: Lacey, WA
 
JADAV wrote:
... Should the semicircle be at a scale say as large as the Earth, ...

But the semicircle depicted was not at that scale. Even if you had a semicircle that large, the picture would deviate from a straight line after only one pointy. Just because it looks like a straight line to an observer doesn't mean that it is straight; the observer simply does not have tools hat are precise enough measuring the angle.

Mar 1, 2021 04:55:31   #
JADAV
 
TheShoe wrote:
But the semicircle depicted was not at that scale. Even if you had a semicircle that large, the picture would deviate from a straight line after only one pointy. Just because it looks like a straight line to an observer doesn't mean that it is straight; the observer simply does not have tools hat are precise enough measuring the angle.


What is true at one scale for a semicircle holds true at any other scale. The arc of a semicircle meets the diameter at 90 degrees, and begins to deviate immediately, but the right angle still exists. If a target was placed at the end of the diameter and a bullet was measured to have struck it at a right angle it would still have travelled in a curve as all projectiles do under gravity. It might be helpful to look at a definition:

"Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint. The point at which the two rays meet (intersect) is called the vertex."

It doesn't state that the lines have to be straight lines.

At the same scale of the Earth at the Equator the arc of the circle will turn through a single degree over 69.172 miles and I'd guess that most tools for setting out buildings, until recently, have not been constructed to that level of accuracy.

Mar 1, 2021 07:20:18   #
Dannj
 
JADAV wrote:
What is true at one scale for a semicircle holds true at any other scale. The arc of a semicircle meets the diameter at 90 degrees, and begins to deviate immediately, but the right angle still exists. If a target was placed at the end of the diameter and a bullet was measured to have struck it at a right angle it would still have travelled in a curve as all projectiles do under gravity. It might be helpful to look at a definition:

"Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint. The point at which the two rays meet (intersect) is called the vertex."

It doesn't state that the lines have to be straight lines.

At the same scale of the Earth at the Equator the arc of the circle will turn through a single degree over 69.172 miles and I'd guess that most tools for setting out buildings, until recently, have not been constructed to that level of accuracy.
What is true at one scale for a semicircle holds t... (show quote)


And a 7 year old will understand that?😳

 
 
Mar 1, 2021 23:50:28   #
n3eg Loc: West coast USA
 
george19 wrote:
The answer involves math beyond the ability of a seven year old to understand. Yes, technically there are two right angles in the figure, but they are made by the instantaneous tangent at the intersections, developed from an infinitesimal delta there, i.e., calculus. This question is inappropriate for even most high school students.

And there you have the correct answer.

Mar 3, 2021 18:56:16   #
joecichjr Loc: Illinois, USA
 
twosummers wrote:
This article appeared in a UK newspaper yesterday - a UK University Maths lecturer does not know how to advise his seven year old daughter when she was given this problem at school. What would your advice be? IS it maths or philosophy or even maths philosophy?


I think most kids would know that. I wouldn't have at that age, but many would.

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