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Need geometry problems

Piscivore

Smelling fishy
Piscivore
Joined
May 18, 2004
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As I mentioned in another thread, I'm giving it a go at teaching myself calculus. Right now, I'm reviewing Geometry. What I need is an online source for problems I can work for practice, my book budget for the quarter having been totally used up. Anyone have recommendations?
 
You might try using library books... or do online searches for homeschool materials.

I found a couple here:
http://www.homeschoolmath.net/math_high_school.php

and here:
http://www.mathsnet.net/geometry/index.html

and there is the Mathforum place... it might have some stuff:
http://mathforum.org/students/ with this:
http://mathforum.org/library/problems/geometry.html
(which unfortunately require a paid membership).

It does look like things that used to be available for free years ago when I was looking around for them, now require fees.

I don't know about your area... but the summer usually has lots of garage sales. You might check to see if some places have geometry texts for sale cheap (the really BIG library foundation book sale has a whole section of textbooks). ALSO... there are stores that sell educational computer software very cheap -- it is usually out of date version-wise, but the information is still valid.
 
Search google for Doron Zielberger and Antreas P. Hatzipolakis and his list Hyacinthus.

I don't know what you need but a classic and cult of Zielberger is this one and if I recall correctly Shalosh Ekhad is the name he has given to his laptop! :)
 
http://sosmath.com/ (Watch the pop-ups)

After about nine years of not being able to store certain aspects of Trig in my head for whatever reason, I found this source while looking for a nice, easy reference. I like mathworld.wolfram.org, I really, really do. Some of the stuff feels just outside my current grasp though. Math is generally easier for me to learn in a classroom setting when it comes to the precise and nigh-esoteric language of it. But it's fun.

BTW, geometry and calculus are my favorite maths. Sadly, my geometry was just over ten years ago, so all I really remember are a few things and loving proofs.
 
Just for fun, here's one of my own :)

In the attached diagram, Line AB and Line AC are both tangent to Circle D from the point A. B and C refer to the points where the lines contact the circle.

Prove that the measure of the included minor arc of circle D (arc BC) is equal to 180 minus the measure of the angle BAC.

Of course, I'd imagine you were looking for more along the lines of trig and such, but hey, I figured this one out in my 10th grade class, and dangit, I'm proud of it :P

Heh

Dammit, just realized I can't upload an image file.

Okay, hopefully you can draw it from the description, though. You have two lines (AB and AC) tangent to the same circle (D) from a single point (A). Looks like an ice cream cone :)
 
Also, for fun you can find an old CAD (Computer Aided Design) program and play (I used to use Generic CADD ... and I have a version of Visual CAD somewhere)...

But what is cheaper and more intuitive to learn geometry is to get a hold of the basic equipment:

1) Straight edge

2) compass (the tool used to make circles, not the thing with the needle that points north).

Editted to (because the Mathworld place is so cool) -- like THESE constructions:
http://mathworld.wolfram.com/GeometricConstruction.html

and start drawing... then add to the basic drafting tools:

3) 30/60 triangle

4) 45 degree right triangle

6) protractor

And then play with some of the figures in Wolfram's Mathworld... like this one:
http://mathworld.wolfram.com/AngleBisector.html

(I love that site... you can use the links to learn about all sorts of things).
 
P- One for later. How do you get two mountain bikes in a VW Golf?


Now how do you get them OUT?

I find mathematics fails when presented with real world prblems of this complexity. ;)
 
Soapy Sam said:
P- One for later. How do you get two mountain bikes in a VW Golf?


Now how do you get them OUT?

I find mathematics fails when presented with real world prblems of this complexity. ;)
Click to expand...

Well you see, the mathematics are still working there on an unconcious level of your brain. You're calculating what the hell you were thinking trying to get anything of that size into a VW vehicle.:p
 
LostAngeles said:


Well you see, the mathematics are still working there on an unconcious level of your brain. You're calculating what the hell you were thinking trying to get anything of that size into a VW vehicle.:p
Click to expand...

And why he was too cheap to buy and install a bike carrier.

(this is funny in a coincidental kind of way... since yesterday I was helping my neighbors get some garden sculpture out of their VW Jetta)
 
Trying to prevent them bing pinched, while trying not to wreck the car interior. They do go in, but then seem to merge into one hyperbike, which has to be rotated through five dimensions to get out.

On topic- there must be loads of simpler space filling problems around. Perhaps Piscivore could design his own using regular shapes, like toy blocks, rather than a CAD program?
 
Piscivore said:
As I mentioned in another thread, I'm giving it a go at teaching myself calculus. Right now, I'm reviewing Geometry. What I need is an online source for problems I can work for practice, my book budget for the quarter having been totally used up. Anyone have recommendations?
Click to expand...

Feel free to post/PM/email any questions you may have in your study of geometry/calculus/math. :)
 
Huntsman said:
Just for fun, here's one of my own :)

In the attached diagram, Line AB and Line AC are both tangent to Circle D from the point A. B and C refer to the points where the lines contact the circle.

Prove that the measure of the included minor arc of circle D (arc BC) is equal to 180 minus the measure of the angle BAC.

Of course, I'd imagine you were looking for more along the lines of trig and such, but hey, I figured this one out in my 10th grade class, and dangit, I'm proud of it :P

Heh

Dammit, just realized I can't upload an image file.

Okay, hopefully you can draw it from the description, though. You have two lines (AB and AC) tangent to the same circle (D) from a single point (A). Looks like an ice cream cone :)
Click to expand...
Here's a way:
1) Draw radii BD and BC. They are, of course, equal to one another.

2) ABD and ACD are right angles because tangent lines always create right angles with radii.

3) Draw line AD, creating triangles ABD and ACD.

4) The two triangles are equal because of hypotenuse-leg.

5) ADB=ADC because of triangle congruency. This means that 2ADB=BDC or (1/2)BDC=ADB. BAD=CAD by triangle congruency. Therefore, 2BAD=BAC or (1/2)BAC=BAD

6) ADB + BAD=90 by the sum of angles in a triangle (I hope it's understood that I subtracted the right angle, but it doesn't have to be, cuz I wrote it here).

7) Using the equivalencies established in step 5, (1/2)BAC + (1/2)BDC=90. Multiply both sides by 2. This gives us BAC + BDC=180. Rearrange the equation and you get 180 - BAC=BDC
 
Huntsman said:
Just for fun, here's one of my own :)

In the attached diagram, Line AB and Line AC are both tangent to Circle D from the point A. B and C refer to the points where the lines contact the circle.

Prove that the measure of the included minor arc of circle D (arc BC) is equal to 180 minus the measure of the angle BAC.

Of course, I'd imagine you were looking for more along the lines of trig and such, but hey, I figured this one out in my 10th grade class, and dangit, I'm proud of it :P

Heh

Dammit, just realized I can't upload an image file.

Okay, hopefully you can draw it from the description, though. You have two lines (AB and AC) tangent to the same circle (D) from a single point (A). Looks like an ice cream cone :)
Click to expand...
Here's another way:

1) Draw BD, BC, and DC.

2) ABD and ACD are right angles because of tangency of lines AB and AC.

3) ABC + DBC=90 by angle addition. ACB + DCB=90 by angle addition. ABC +DBC +ACB + DCB=180 by angle addition.

4) BAC + ABC + DBC + ACB + DCB + BDC=360 by sum of angles of triangle (in this case, we have two triangles, so the sum is 360).

5) By substitution, BAC + 180 + BDC=360. BAC + BDC=180. Rearrange and get 180 - BAC=BDC.
 
Here's a nice little geometry problem I remember. It doesn't actually take a lot of geometry knowlege, but it may take a fair amount of thinking to figure out.

Take an arbitrary triangle, and inscribe an elipse so that the edges of the elipse touch all three sides of the triangle but it remains completely inside the triangle. What is the maximum ratio of elipse area to triangle area (that is, how much area inside the triangle can you fill up with the elipse)?
 
Piscivore said:
As I mentioned in another thread, I'm giving it a go at teaching myself calculus.
Click to expand...
I couldn't find this post of yours and out of mere curiosity I wonder what made you take this decision. :)
 
Re: Re: Need geometry problems

Esther said:
I couldn't find this post of yours and out of mere curiosity I wonder what made you take this decision. :)
Click to expand...

I was one of those kids who got "taught" by the public school system that I "just wasn't good at math". I want to fix that.

Besides that, when I pick up "Gravity's Rainbow" again, I want to know what the hell Pynchon's talking about. :)
 
Interesting. :)

People say that in 9 out of the 10 cases of the students that they were not strong in Maths at school there is a teacher to blame.

To your confort I quote the famous anecdote Feynman used to say to his audience about quantum mechanics but it applies to maths as well.
"You don't
understand it? Well, I am afraid you cannot understand it. Look, I have graduate students who worked with me for five years, and they
still do not understand it. Do you want to know why? Because I myself do not understand it either!"
Click to expand...

;)

As for "Gravity's Rainbow" personally I consider it a must read for the students of history and not for the students of science but as people who know me say, I have twisted tastes.

Seriously, very few people can read Pynchon without the "key" that explains all those innuendos and references. It's a great book to understand the post-war periods. Soon it will become a best-seller again in USA.

Edited to add( part two): Don't get me started with Pynchon :) Find the "companion" or " guide" to "Gravity's Rainbow".It's easier than catching up with Maths.

You know, all the details he mentions, about the BBC's shows, the theatrical plays and stuff are real, they have double-checked them with the newspapers of the era!! Pynchon is a genuine "paranoid".
 
Funnily enough, I realize that I'm not particularly good at math, but I do enjoy it, thanks to three particular math teachers who were fun, enjoyable, sadistic, and out right nuts.

And I do have to start reading "Gravity's Rainbow again.
 
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