Math Question
- Thread starter stugotsms
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Wait a sec Winston.... if you fold the paper in half you get a semicircle..... now are you saying that if you draw a line extending from the center at 60 degrees and 120 degrees creating 2 radii? Because that sounds like you are creating a wedge that is 120 degrees wide a la a pac man shape.
You're method only works if you count the fold as a line which in my mind is too abstract and unfair of a question.
If its straight lines with no bends I can't see how to create 6 equal parts.... I think you need 3 lines..... 3 diameters each being 60 degrees apart.
You're method only works if you count the fold as a line which in my mind is too abstract and unfair of a question.
If its straight lines with no bends I can't see how to create 6 equal parts.... I think you need 3 lines..... 3 diameters each being 60 degrees apart.
I've no idea how to even start answering that question, yet I still make six figures!! Yay, I beat the math demon by avoiding it altogether. I wish I could go back in time and throw my pay statement into my calculus teacher's face, chanting "How will this help me in the real world? How will this help me in the real world?" like some kind of possessed math-hating zombie.
Oh yeah, and so long as I'm back in high school, I may as well nail a couple young hotties before I return to 2005.
"....if and only if..........." What the hell was that?
Oh yeah, and so long as I'm back in high school, I may as well nail a couple young hotties before I return to 2005.
"....if and only if..........." What the hell was that?
The question can be answered, and in fact, I did it with only one line. However, it takes a little creative thinking and requires not falling into the trap that "line" means "straight line". To do it, simply divide the circle into six pieces as you would with three straight lines, but rather than lift your pencil when you hit the edge with a line, simply go outside the circle, loop around, and basically start the next straight line.
i don't like the "fold the paper" answer, because nothing in the question suggests that the circle needs to be on paper. it could be a crop circle, a circle written on stone, etc. to assume paper is to assume something not given.
given that this is a grade 7 textbook - an age where most students struggle with very basic geometry - i highly doubt that they were looking for a creative answer. thus, while the question can be solved, based on the intended audience i would conclude that the question has an error in it.
i don't like the "fold the paper" answer, because nothing in the question suggests that the circle needs to be on paper. it could be a crop circle, a circle written on stone, etc. to assume paper is to assume something not given.
given that this is a grade 7 textbook - an age where most students struggle with very basic geometry - i highly doubt that they were looking for a creative answer. thus, while the question can be solved, based on the intended audience i would conclude that the question has an error in it.
P_B is right, but I think they want you to use two lines to think outside the box.
One line is a continues figure 8 with the cross point being straight lines at the center of the circle and the loops being made on the outside of the circle. The second line is a single straight line through the center/middle of the figure 8 cutting it in half.
One line is a continues figure 8 with the cross point being straight lines at the center of the circle and the loops being made on the outside of the circle. The second line is a single straight line through the center/middle of the figure 8 cutting it in half.
The question was not in error. It was to open you minded to the idea that a line is not always from point to point. I once had a math question that the teacher asked us to calculate how many steps you would need to take in the class-room to reach the middle of the class. Each step was always half of the space you needed to get too.
While my classmates were trying to count steps I drew a sideways figure 8 and handed that in as the answer. Infinity, it can’t be measured but it is a line. If each time you cut something in half you will always have another piece to cut again.
While my classmates were trying to count steps I drew a sideways figure 8 and handed that in as the answer. Infinity, it can’t be measured but it is a line. If each time you cut something in half you will always have another piece to cut again.
Providing you can move the lines.....
Next, take the radius and keep one ned fixed and move the other end so that it intersects the circle at another point on the circumference and mark that point. Continue moving the line until the end of the line meets up with the point at which you started. If you have done all of this in a neat and accurate manner, your line will meet the first point, and you will have six points on the circumference of the circle. Cut the circle from the points on the circumference to the centre, and you have six equal pieces.
Try this on pumpkin pie for Haloween.
shakenbake
Really, you only need to use one line as a 'tape measure'. Draw a straight line from the centre of the circle to the perimeter. This is the radius. Now, you need to move this line around the circumference of the circle. You take the radius, and put it anywhere onto the circle so that both ends touch the circumference. Mark these points where the line intersects the circumference.stugotsms said:This is out of a grade 7 math book. How do you split a circle in 6 equal pieces with two lines?
Any ideas?
Next, take the radius and keep one ned fixed and move the other end so that it intersects the circle at another point on the circumference and mark that point. Continue moving the line until the end of the line meets up with the point at which you started. If you have done all of this in a neat and accurate manner, your line will meet the first point, and you will have six points on the circumference of the circle. Cut the circle from the points on the circumference to the centre, and you have six equal pieces.
Try this on pumpkin pie for Haloween.
shakenbake
Draw a circle. Draw a sine wave starting at 240 degrees up to the invert and back down to 120 degrees. Draw a cosine wave (inverted sine wave) starting at 300 degrees that bisects the sine wave twice but not touching the bottom of the outer circle (otherwise you would get 7 segments). Six segments. The real math comes from solving the quadratic equations to solve for amplitudes of the parabolic curves that results in equal areas under the bisected parabolas. A little beyond 7th grade I think.
Sorry shakenbake and plunker but way to complicated.
It is just a mater of dividing the circle into six segments, 360/6=60degree angles. Now we start to draw our infinity symbol entering the circle at the 60-degree mark and exiting at the 240 point. Continue to loop the line up and return into the circle at the 300-degree point and exit at the 120 point. Close this loop by returning to the starting point of 60 degrees; this is the first line. The second line is straight up and down from the 360/0 point to the 180-degree point. Two lines, 6 pieces.
It is just a mater of dividing the circle into six segments, 360/6=60degree angles. Now we start to draw our infinity symbol entering the circle at the 60-degree mark and exiting at the 240 point. Continue to loop the line up and return into the circle at the 300-degree point and exit at the 120 point. Close this loop by returning to the starting point of 60 degrees; this is the first line. The second line is straight up and down from the 360/0 point to the 180-degree point. Two lines, 6 pieces.
Q. How do you split a circle in 6 equal pieces with two lines?
how about take two lines at a 60 degree angle from each other. use this as a template to cut the circle into six pieces. the question doesn't say to draw the lines in the circle - just to split a circle with two lines.
how about take two lines at a 60 degree angle from each other. use this as a template to cut the circle into six pieces. the question doesn't say to draw the lines in the circle - just to split a circle with two lines.
I really like justajohn's answer, but my old Geometry teacher would have said, "Fine, now show me the proof". That 'infinity symbol' would have to be defined as having straight-line portions from the circumference to circumference as it crossed the circle. At which point [hehe—Euclidean humour] he would have said, "Ah, you mean a figure composed of two straight lines crossing at their mid points whose outer ends are joined by two additional curved lines". But if by line you mean everything a pencil draws before you lift it off the paper, or think you can use Algebraic Geometry to define that infinity symbol, well …
