On Tuesdays I upload an update of what we did in math for the week.

RightStart Geometry:

Lesson 73 The Amazing Nine-Point Circle

“In 1822 a German mathematician, Karl Feuerbach, showed that the nine-point circle is tangent to the inscribed circle. [....] Because of his work, this circle is known in Germany as the Feuerbach circle.”

So, folks in Germany apparently sit around talking about the Feuerbach circle, eh? Shoot, I don’t believe I’ve ever heard of this before. Given all of the history (two Frenchmen did the original proof) I’m not sure how I missed out. Hmmm.

Kid1 has problems keeping track of what she is looking for. I am called upon to explain that

*XO*is a line segment rather than an angle, for example. Over the course of the next few lessons she will get better at this, I’m sure.

Lesson 74 Drawing Arcs

Kid1 is content drawing hearts, interstate signs, radiation warning signs, and a gothic arch. Math meets art. What could be better?

Lesson 75 Angles ‘n Arcs

The lesson teaches inscribed angles and intercepted arcs. It bandies terms like “chord”. I’ve never been too terribly fond of this stuff, and Kid1 seems to be following in my footsteps. Mostly I hope she figures it out and doesn’t ask me too many questions.

Lesson 76 Arc Length

Problem 1 on the worksheet involves finding the length of an arc to the nearest tenth of a centimeter. Both Kid1 and I measure the angle from the center of the circle to the arc ends repeatedly; we do NOT get the measure shown in the answer sheet. This means that Kid1 can NOT get the same final answer for the length of the arc as the answer sheet.. Her work shows the same steps, though -- the answer sheets give the steps for figuring out each problem.

Problem 2 features a gothic arch. I sort of blanch when I see it, but Kid1 acts like

*everyone*knows the way a gothic arch is formed, for heaven’s sake. She explains it to me; I immediately forget.

Problem 4 is finding the distance from Earth’s poles to the equater. It reminds me of something out of Challenge Math, or some other such math book. It takes a moment for Kid1 to “get” that working in 3D isn’t too terribly different from working in 2D.

Problem 5 is a landscaping problem. I tend to dislike these, mostly since I studied landscaping in college and find myself questioning why the heck someone would want to put

*that*in their yard. I mean, really, why would Morgan want to put bricks around a circular garden? Why not something else? What type of bricks? Will she be interplanting moss between the bricks? Will she be levelling these so she can mow easily around it? And how did she end up running out of bricks? Did she not plan? If that’s the case (that she didn’t plan for how big a circle she needed to make) it’s entirely possible that she did not plan well for plant spacing (a pet peeve of mine).

On the bright side, Morgan is working with the metric system, so when she runs short by .7 meters it’s easy to figure out how many bricks she needs (although Kid1 points out that the inside of the brick circle is a different measure than the outside, since bricks aren’t actually wedge shaped -- woohoo, that’s my girl!).

After finishing problem 3 (trefoils and quatrefoils, which are apprently as easy as gothic arches; problem 3 falls at the end for Kid1 because of the way the problems are laid out on the page), there is an option of writing a paper on the metric system. We have discussed the metric system some during the course of the lesson. Kid1 declines writing a paper.

Somewhere in the course of this lesson I realize that she needs a refresher on multiplying fractions.

Lesson 77 Area of a Circle

For the second work sheet the student figures out the width of a parallelogram as it relates to the diameter of a circle. The width is equivalent to half the circle’s diameter, but Kid1 is mortally offended that the width is therefor pi r. She says it’s just plain wrong -- she agrees that it is half of 2pi r, but feels that saying “pi r” is somehow vile and unnatural.

You can imagine what happens when she has to cut up the circle and lay it on top of the parallelogram ... the parallelogram has a height of r ... she is supposed to give the area of the circle ... sure enough, she writes” r pi times r”. She refuses to call it pi r squared. Whatever. When she was young she was mortally offended that the indefinite article used before a word that begins with a vowel is "an", and vowed never to use it as long as she lived, and to strive to convert others to her way of thinking. This is likely to be another such case.

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