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A bit of googling this morning made sense of yesterday's mystery: the key word was "three," and the sentence needs rearranging. What they're trying to say, I think, is "when three lines meet at a point, they are called concurrent." Which is not a neologism, but doesn't match the other meanings of "concurrent," which were used in several previous lessons, so I hope the editor will make that (or some similar) change, so the students will see "this is an additional meaning of the word" rather than wondering what it means to say lines are the same length (that being what "concurrent" means for line segments).
This is a lead-in to stuff about triangles and the intersections of their angle bisectors, etc., which lurk under names like "incenter" and "orthocenter" and "circumcenter" (the circumcenter of a triangle is not always within the triangle). I suspect that the bit about concurrent lines could be deleted without any loss to understanding, but I'm not editing this book.
Someone asked, in response to yesterday's post, what I like about working on the algebra books, and why they bother issuing new geometry books, because aren't they all more-or-less literal translations of Euclid's Elements, since there's nothing new in geometry.
The short answer to the first includes that I like helping get things right, and that in some moods I enjoy things like factoring quadratics and getting paid for it. For the second, there are several answers, including "there's quite a bit new in geometry, and a little bit of it even turns up at the high school level." However, while I like tesselations, they don't lead much of anywhere, and I'm not convinced the addition of the "kite" to the list of standard quadrilaterals is an improvement. Trigonometry, which is a significant part of high school math and at least some of which is in geometry, is not in Euclid. Non-Euclidean geometry, which is also not in Euclid, is well beyond the scope of what we're being asked to cover, even though our world is not in fact a plane. Other answers (in addition to "because people want to buy the books," which is non-trivial: if nobody would buy them, we wouldn't bother producing them) include that different books emphasize different subsets of mathematics, and that even if the ideas or results are the same, there may be different good ways of teaching them, in different contexts and for different learners.
This is a lead-in to stuff about triangles and the intersections of their angle bisectors, etc., which lurk under names like "incenter" and "orthocenter" and "circumcenter" (the circumcenter of a triangle is not always within the triangle). I suspect that the bit about concurrent lines could be deleted without any loss to understanding, but I'm not editing this book.
Someone asked, in response to yesterday's post, what I like about working on the algebra books, and why they bother issuing new geometry books, because aren't they all more-or-less literal translations of Euclid's Elements, since there's nothing new in geometry.
The short answer to the first includes that I like helping get things right, and that in some moods I enjoy things like factoring quadratics and getting paid for it. For the second, there are several answers, including "there's quite a bit new in geometry, and a little bit of it even turns up at the high school level." However, while I like tesselations, they don't lead much of anywhere, and I'm not convinced the addition of the "kite" to the list of standard quadrilaterals is an improvement. Trigonometry, which is a significant part of high school math and at least some of which is in geometry, is not in Euclid. Non-Euclidean geometry, which is also not in Euclid, is well beyond the scope of what we're being asked to cover, even though our world is not in fact a plane. Other answers (in addition to "because people want to buy the books," which is non-trivial: if nobody would buy them, we wouldn't bother producing them) include that different books emphasize different subsets of mathematics, and that even if the ideas or results are the same, there may be different good ways of teaching them, in different contexts and for different learners.
