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#1 2011-11-27 00:20:16
- bobbym
- Administrator
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Circles.
In the drawing below each little circle has a circumference of pi units. They also meet at only 1 point with each of the two other smaller circles. The center of each small circle is on the circumference of the red circle.What is the radius of the red circle?
See http://www.mathisfunforum.com/viewtopic … 2&p=47
Post #1174.
1) Use the circle with center and radius tool to make a circle with center at the origin and with a radius of 4 units.
2)Expand or shrink the screen until the circle looks round and is large enough.
3) Color the circle red.
4) Put another circle at B that has radius of .5 and another at C. See the diagram.
5)Fill in by putting 4 more circles between the two small ones you already have,
6)Put them one in each quadrant.
There is lots of room isn't there? Go into the object properties of the red circle and find this statement.
Circle[A, 4] change it to Circle[A, 1]
Do some minor adjusting until the circles fit well.
What do you observe? Use the measuring tool and measure line segment AB. You will get 1. Pretty strong evidence for the answer of radius of the red circle is 1.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#2 2011-11-27 05:02:55
- phrontister
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Re: Circles.
Hi Bobby,
I downloaded & installed GeoGebra; and yes, that works.
For the adjusting process I found it easier to have the small circles as 'dependent objects' on the red circle, which you can do by placing the centre point of the small circles onto the red circle's circumference.
That enables group adjusting simply by altering the red circle's size. The positions of the small circles in the quadrants can then easily be adjusted around the red circle (the two x-axis circles are correctly repositioned automatically when the red circle is resized).
I don't know how to change a 'free object' into a dependent one, so once I saw the advantage that dependence would bring for this task I started again from scratch.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#3 2011-11-27 05:13:19
- bobbym
- Administrator
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Re: Circles.
Hi;
I am glad you did.
If you use the center with radius tool and put the centers on anything other than the axes ( but still on the red circle ) they will be semi - free objects. This means they can move anywhere on the circles circumference. This is exactly what you want for this example.
If you have the time check out my tuts in that thread. I know they are pretty clumsy but I have used them to answer tough geometry questions here and elsewhere.
Which version did you install?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2011-11-27 11:00:40
- phrontister
- Real Member
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Re: Circles.
Hi Bobby,
My version is 4.0.10.0, for Windows.
I'll have a look at the tuts when I have more free time...thanks.
What do you observe? Use the measuring tool and measure line segment AB. You will get 1.
Also, the radius displays when right mouse-clicking the circumference.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#5 2011-11-27 11:07:39
- bobbym
- Administrator
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Re: Circles.
Hi phrontister;
Yes, I know about that.
I'll have a look at the tuts when I have more free time...thanks.
Do not thank me yet, I was hoping to get a couple of pointers from you.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2011-11-27 12:05:03
- phrontister
- Real Member
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Re: Circles.
bobbym wrote:
If you use the center with radius tool and put the centers on anything other than the axes ( but still on the red circle ) they will be semi - free objects. This means they can move anywhere on the circles circumference.
In this case at least, that seems to be the only means of enabling points that are on an axis to move like the others. I can't get them to detach from their axis, and they'll only move if the object on which they are dependent moves.
Another feature I'd like - and it gets a mention on the help pages but doesn't seem to have been implemented yet (unless I've missed it) - is to have a SnapToObjects function for snapping objects to objects (like in M$Word). I think you can only snap points to grid now.
Maybe these might help in some situations too:
- Snap points to objects;
- Snap points (and objects) to grid lines (not just to grid intersections)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#7 2011-11-27 21:50:23
- bobbym
- Administrator
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Re: Circles.
Hi phrontister;
To make a dependent point free do this:
1) Use the point tool to put a point on the x axis. It will look like the first picture. You can only move it right and left. That is because it is a dependent object. Check the Algebra pane to see that.
To get it to be a free object, right click the point. Click object properties. A box will open up and in the basic tab you will see "Point[xAxis]" in definitions. Delete that and enter (2,0). If the new definition does not hold try again.
When you are successful you will have a point A under Free objects in the Algebra pane. You can now move the point around.
This is one way to free any point. Remember that the idea of having a dependent object is so when the parent changes so will the child object.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2011-11-28 07:13:59
- phrontister
- Real Member
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Re: Circles.
Hi Bobby,
Yes...it freed the dependent point. Thanks.
Trying it on the circle problem with the small circle that's at (-1,0), it frees the circle from both its parent red circle and the xAxis.
To only free it from the xAxis I double-clicked its point and changed the definition (is that what it's called?) to "point[c]". That freed it from the xAxis and placed it on top of the small circle that's already at (1,0), while maintaining its dependence on the red circle.
From there it can be moved along the red circle's circumference back to its possie at (-1,0).
Maybe the program could do with a freeing option.
Edit: Just installed the latest update. There's an "Attach/Detach Point" button in the button bar now. Was that there before?. It works well. You can also do it from Attach/Detach Point in Tools/Point Tools.
Last edited by phrontister (2011-11-28 08:46:12)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#9 2011-11-28 08:44:27
- bobbym
- Administrator
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Re: Circles.
Hi phrontister;
The last couple of versions have had an attach detach button. I have been unable to get it to work for everything.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#10 2011-11-28 08:47:30
- phrontister
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Re: Circles.
My edit to my previous post crossed with your post.
I've only tried it on the circle problem.
EDIT: I've just noticed that my previous version had the menu item function, but not the button.
Last edited by phrontister (2011-11-28 08:52:22)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#11 2011-11-28 09:00:53
- bobbym
- Administrator
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Re: Circles.
Hi;
I have 4.1.22.0. On the pull down menu ( 2nd button on top ) there is a attach/detach button.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#12 2011-11-28 09:19:47
- phrontister
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Re: Circles.
Ah yes...so there is. Didn't see that there before.
I've worked out what that toolbar does now. On startup it loads the first button in the toolbar's pull-down menus, and subsequently retains any pulled-down buttons for the buttons that show in the bar.
That also happens when you access a toolbar item from the Tools menu...which is what I must have done earlier to get that icon to show on the toolbar.
I have 4.0.11.0 now.
Last edited by phrontister (2011-11-28 09:35:11)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#13 2011-11-28 10:23:07
- bobbym
- Administrator
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Re: Circles.
Hi;
You have the smaller download. It does not contain the Maxima package. That is the only difference. Same geogebra as mine.
It has a lot of nice features have you seen this?
http://www.mathisfunforum.com/viewtopic.php?id=16928
All done with geogebra.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.