Maths Education and Rational Trigonometry (II) | WildTrig: Intro to Rational Trigonometry

Mathematics education is in sore need of some serious analysis and revision: not with regard to how to teach mathematics, but rather with regard to what we teach! It is so important to not have a fixed idea about the optimal sequence of topics.

Here we begin a discussion about alternative ways of teaching trigonometry, and geometry, to primary school students. We want to separate the study of triangles and circles. We want to let go of the need of using distances and angles for all our measurements. And we want a measurement system that is consistent with the Cartesian coordinate framework introduced in the 17th century.

Quadrance and spread work within the Cartesian coordinate system, not against it!

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Here are the Insights into Mathematics Playlists:

Here are the Wild Egg Maths Playlists (some available only to Members!)

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[OldSloGuy]

The Egyptians were on to something, slopes measured in run per unit rise rather than a decimal fraction (%). A still water surface will define level. If your primary concern is drainage in a river valley like the Nile, the land is nearly flat in those places people find convenient to their purposes. A 0.5 % slope becomes 200, an integer and real number, avoiding fractions. Architecture tends to be rectangular with vertical walls and flat floors, the need for slopes is minimal. Pyramids are an exception. Columns are usually round and since most roofs have disappeared, we don't know if the columns supported anything. From a structural consideration, corners form stress concentrations during the column erection process, particularly if slings or ropes are used, hence a preference for round columns.