Color the quarter

shahar

shahar

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I need to color 1/4 of every figure.
What is the easiest way to do it?
Only by straightedge (in way of compass and straightedge building)?
 
One approach: divide each shape into a number of regions of equal area, color 1/4 of them.
 
I'd use symmetry.

Each of these (assuming that it is exactly what it looks like, namely a regular polygon) has a line of symmetry; draw that to divide it in two.

Then each half, in every case but the second, also has symmetry, so you can just repeat the process.

There is a different trick to easily divide each half of the triangle into two equal parts. Can you see it? Let me know!

By the way, the word, instead of "building", is "construction".
 
O.K. I need a rest from what going on the visit of my parents house.
I look it in the next few days.
There is no place to go. Only, to buy products to cook food or to order pizza by phone.
All the shops, restaurants are closed and those that open get a fine and etc. and etc.
 
fourfig.png
From left to right: I) bisect the two vertical sides and then draw the vertical diagonal.
II) Bisect each vertical side and connect the midpoints.
III) draw the four diagonals.
IV) draw the two diagonals.
 
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I think that you do not have to 1st divide the triangle in half but rather divide it into 1/4s right away.

EDIT: pka beat me to it and actually showed the partition.
 
Jomo said:
I think that you do not have to 1st divide the triangle in half but rather divide it into 1/4s right away.

EDIT: pka beat me to it and actually showed the partition.
Click to expand...
True; I was trying to get shahar thinking for himself, and starting them all the same way was a reasonable way not to give away an answer.

My solution for the triangle would better illustrate the fact that quarters don't have to be congruent: I'd have three lines fanning out from the midpoint of the base. But yours is, of course, prettier. I'm not positive which is "easier".

shahar said:
There is no place to go. Only, to buy products to cook food or to order pizza by phone.
All the shops, restaurants are closed and those that open get a fine and etc. and etc.
Click to expand...
It's the same here in New York state. My college has gone to fully online (I'm lucky enough to be teaching only in fall semesters, so I've escaped that scramble), and my tutoring center is doing likewise. Either way, there's lots of work to do but no place to escape to (except more online, or outdoors when it gets warmer).
 
Dr Peterson, are you saying that the walk-in tutoring center you work in is now online? Wow!
 
Jomo said:
Dr Peterson, are you saying that the walk-in tutoring center you work in is now online? Wow!
Click to expand...

It's just being set up, and we'll see how it works on Monday. I expect a fairly slow learning curve, like the start of a new semester. (We've been closed this week to prepare for the new world, and are using TutorOcean as the basis for the site.)

I don't think it will work like a walk-in yet, but as we learn how the site works, I hope it will be good enough for students who are used to working in groups and raising a hand to ask a question.

I'd suggested other (poorly formed) ideas, but the school went for this for its appointment-based tutors, and we went along. (I'm not in charge!)
 
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