Is the the most baffling geometry question ever posed for a 7 year old pupil?
Feb 27, 2021 09:16:41 #
Don's Leica
Loc: Asheville, NC
I would answer yes two right angles: if I were a bug crawling around the semicircle, when I met the straight line across the diameter of the circle, I would be traveling perpendicular to it. I believe little kids can see the world through their small friends' eyes. Or, think of driving your little toy car around a circular dirt road in the dirt, like I did when I was 7. When you meet the straight line road, you need a right turn or left turn of 90 degrees.
Feb 27, 2021 09:52:42 #
At it's most literal, It's geometry.
No doubt the diagram was presented at a small human scale
and if one presumes, for academic sake, that the diagram
is perfect then Robert Jerl is correct imo.
HOWEVER!
If the hemisphere (hemicircle?) had a 1000 mile radius,
and a carpenter wanted to put
a cupboard for his tools in that "corner"
with it's sides parallel to the lines
that defined that corner, and measured the "angle"
where the lines intersect with his protractor
which he bought from the local hardware store, it would be a
nice accurate right angle.
No doubt the diagram was presented at a small human scale
and if one presumes, for academic sake, that the diagram
is perfect then Robert Jerl is correct imo.
HOWEVER!
If the hemisphere (hemicircle?) had a 1000 mile radius,
and a carpenter wanted to put
a cupboard for his tools in that "corner"
with it's sides parallel to the lines
that defined that corner, and measured the "angle"
where the lines intersect with his protractor
which he bought from the local hardware store, it would be a
nice accurate right angle.
Feb 27, 2021 10:05:04 #
Sarco wrote:
I believe that there are 4 right angles in the image, the frame is there for a reason, it forms part of the image.
The question refers to the half-circle shape, not the frame. Following your logic I’d say there would be 12 right angles: 4 each formed by the interior angles of the two figures (the white box and the purple box surrounding it) enclosing the shape. There would also be 4 exterior right angles at the corners of the purple box.
Feb 27, 2021 10:31:25 #
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?
If one is looking down at a globe, the answer is that the image actually is that there are two right angles. It's an old math trick question. Parallel lines meet in curved space. If the straight line is viewed as the Earth's equator, the center of the curve is the North pole. So both sides of the curve are heading north from the equator and meet at the pole. They are parallel lines that meet in curved space. I'm no mathematician, but does work on a globe.
Feb 27, 2021 10:56:34 #
At each end of the diameter shown construct the derivative of the circumference. It will be at 90 degrees to the diameter.. This quantity is dC/dR.
Feb 27, 2021 11:13:04 #
Lots of great answers here from the mathematicians BUT we’re talking about 7 year old kids, first-graders. Very few, if any, would understand the concept of angles.
Feb 27, 2021 11:18:00 #
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.
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.
I agree with all but the last statement.
Feb 27, 2021 12:04:03 #
If a vertical line was drawn from a point on the horizontal line downwards you would then have 2 right angles.
Feb 27, 2021 12:14:50 #
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?
That is a bowl. Easy problem.
Feb 27, 2021 12:18:12 #
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?
If a curve is an infinite series of straight lines then an intersecting straight line would result in a right angle!
Feb 27, 2021 12:56:34 #
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?
If a curve is an infinite series of straight lines then an intersecting sraight line forms right angles!
Feb 27, 2021 13:03:29 #
bodiebill wrote:
If a curve is an infinite series of straight lines then an intersecting sraight line forms right angles!
Correct.
Feb 27, 2021 13:26:31 #
No, I would certainly hope not.
Test questions can do two things: To evaluate current knowledge. Good test questions become a learning experience to an inquisitive mind and open a door to continued learning. I don't remember if I knew what a right angle was at age 7. I do know I would have taken it home to my Dad who would have explained it to me and opened the door to geometry long before the 9th grade when some educator had decided I was old enough.
Yeah, I know, that was back in the dark ages when more parents had time for their kids. With just a little encouragement most kids want to learn, my goal was to be as smart as Dad and Mom. Fortunately they wanted me to be smarter than they were.
Test questions can do two things: To evaluate current knowledge. Good test questions become a learning experience to an inquisitive mind and open a door to continued learning. I don't remember if I knew what a right angle was at age 7. I do know I would have taken it home to my Dad who would have explained it to me and opened the door to geometry long before the 9th grade when some educator had decided I was old enough.
Yeah, I know, that was back in the dark ages when more parents had time for their kids. With just a little encouragement most kids want to learn, my goal was to be as smart as Dad and Mom. Fortunately they wanted me to be smarter than they were.
Feb 27, 2021 13:36:45 #
Wyantry
Loc: SW Colorado
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.
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.
Have to agree: the right angles would be at the intersections of the curves with the straight line. These would only be at 90 degrees: a.) if the diagram is that of a true semicircle (the straight line is a Diameter) and, b.) the right angles would be infinitesimal— only approaching 90 degrees as the curve approaches the diameter ends.
Feb 27, 2021 14:07:07 #
robertjerl wrote:
Since right angles are formed by the 90° meeting of two straight lines there are no right angles in this form. It is one straight line intersecting two points of a curved line. No matter how much it looks like two right angles on each end it is not that half circle is curved all the way around.
And I suck at math.
And I suck at math.
An appropriate and honest answer, for a large portion of the popiulation. On the other hand, one could perhaps, argue that there is an infinitely small area at the junctions of the straight line and each side of the semicircle, thus allowing for an extremely small (microscopic) right angle at those intersects.
This is a discussion/debate/argument that could go on for eternity. so I will admit I have a "Devil's Advocate" side that frequently comes to light. Just presenting another possible side and not wishing to get into that eternal debate.
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