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Constructions in Jurgensen (or any) Geometry


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We are doing Jurgensen Geometry and there is a whole chapter (chapter 10) on constructions using a ruler and compass only.  By the very nature of it, it is slow going.  My son wants to know when he would ever need this. LOL.  Even when I did manual drafting in the early 90s in college, we were able to use a triangle at least.  And I would think maybe a protractor also, but I can't remember.  

Is there an online program that would be "faster" for completing these constructions? Or do you just push through? TIA!!

 

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There i was, stuck on a desert island with a piece of bamboo and half of my astrolabe, trying to design a bridge across the estuary to the bustling metropolis on the adjacent island....

Ds did that chapter with DO, but no complaints. I think he was happy to have something that maybe also counted as art but didn't require trying to find the creative side of his brain.

Edited by SusanC
The cake was a lie! 😂
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1 minute ago, SusanC said:

Ds did that chapter with DO, but no complaints. I think he was happy to have something that maybe also counted as art but didn't require trying to find the creative side of his brain.

There has been much weeping and gnashing of teeth here. And since his momma really struggled with manual drafting because she can't see a straight line to save her life, I am very sympathetic.  😃

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Have you looked in the back of the book at p. 710? There are some instructions there for using paper folding techniques. Those sometimes feel more intuitive than the traditional Greek compass and straightedge constructions. It would be a lot shorter than doing the whole chapter if neither of you wants to continue with constructions.

Here's a link that has a few instructions, too. Constructions with Folded Paper - MathBitsNotebook (Geo - CCSS Math)

 

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4 hours ago, cintinative said:

We are doing Jurgensen Geometry and there is a whole chapter (chapter 10) on constructions using a ruler and compass only.  By the very nature of it, it is slow going.  My son wants to know when he would ever need this. LOL.  Even when I did manual drafting in the early 90s in college, we were able to use a triangle at least.  And I would think maybe a protractor also, but I can't remember.  

Is there an online program that would be "faster" for completing these constructions? Or do you just push through? TIA!!

 

We used Geogebra https://www.geogebra.org/?lang=en

the geometry link https://www.geogebra.org/geometry

I am pretty sure my kids use the app on their iPads as well as the website on their windows laptops.

3 hours ago, cintinative said:

There has been much weeping and gnashing of teeth here. And since his momma really struggled with manual drafting because she can't see a straight line to save her life, I am very sympathetic.  😃

I’m sympathetic too and since all my engineering drawings in college in the 90s were done using computer aided design software, I had only used a compass set in elementary school. 
When I had to hand drawn, it was really freehand. 

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We used Geogebra for all geometry constructions as well.

But, it is a good idea to teach how to construct bisectors, use protractors and perform accurate measurements using a ruler. These things are important in the same way as you teach your child to use pencils, erasers, write in cursive even though in adulthood, I hardly ever write on a piece of paper anymore. 

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Thanks! I think we have the basic constructions down. I just would like to speed up these more advanced ones.  I will google geoalgebra.  I figured if there was something that he could use that had a virtual compass, ruler, etc. we could eliminate some of the human error that is causing things to be just a bit off on our manual ones.  

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1 hour ago, Alexinmemphis said:

Have you looked in the back of the book at p. 710? There are some instructions there for using paper folding techniques. Those sometimes feel more intuitive than the traditional Greek compass and straightedge constructions. It would be a lot shorter than doing the whole chapter if neither of you wants to continue with constructions.

I didn't know about the paper folding! I am not sure that would have helped us with this section, but it will help for the earlier ones next time around!

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1 hour ago, cintinative said:

I didn't know about the paper folding! I am not sure that would have helped us with this section, but it will help for the earlier ones next time around!

I wonder if that might be similar to the Patty Paper Geometry approach. I used that with all of my dc as a Pre-geometry class. I taught it to middle grade students at co-op one year.

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We use Prentice Hall, and I don’t think there is an entire chapter on constructions, but of what is there, we do some, read through all, and move on.  No love for it here and it is not worth the time or frustration in my view.  😀

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7 hours ago, SusanC said:

There i was, stuck on a dessert island with a piece of bamboo and half of my astrolabe, trying to design a bridge across the estuary to the bustling metropolis on the adjacent island....

 

Did anyone else see this and picture a kitchen island full of tarts and cupcakes?  (I'm hungry...)

I personally think constructions are fun, but skippable.  Your student may enjoy the Euclidea app for android or apple phones for a gamified version of constructions.   

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I want to add as well that the AoPS textbooks include constructions not in its own chapter but as a short section at the end of several (but not all) of the relevant geometry chapters.  I think doing all the constructions at one time is a bit much.    

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I don't think AoPS text covers loci specifically, but I do remember them in high school math.  I recall a student asserted without proof that the locus of points equidistant from 2 skew lines is a hyperbolic paraboloid.   Seems reasonable.

And I remember we had a school evaluator visit our class on the same day when a student found an error in a locus problem in our textbook.  The teacher had been using it for years and it was the first time someone noticed.  I wish I could remember the problem.  

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I love this chapter myself, and I find the locus problems to be great applications of what you've just been doing in construction. These are questions like, "Given points C and D in a plane, what is the locus of points in that plane 2 cm from C and 3 cm from D?" It brings you back around to the very first example in Chapter 1. There are a lot of diagrams to draw, but it's not as heavy on constructing.  Personally, I don't think 10-8 is necessary if you don't like it. It's nice to have it in there, though, as an extra for people who like constructions (this is my favorite, actually).

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