Teaching connections between Algebra and Geometry II

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[@abajabbajew]

Part 2 (sadly no audio for this part either) I wonder what response you may have found among teachers to the introduction of rational trigonometry (particularly since they now have access to your book)? The problem is your book is written for mature students and the subject - were it to ever progress to a school setting - requires informal treatment (rather like your early WildTrig series) Teachers, as learners of the material, could begin to make up examples such as the '4-5-7' triangle, or try to take ones from real life such as an octagonal parasol design where the central spreads between the panels to achieve a particular 'pitch' must be deduced (and working with paper 'nets' to attempt to create these could lend practicality and enjoyment to the endeavour) Given there is not an actual 4-5-7 triangle in the 2-d plane however, it's not a bad example either, because it leads to the very questions about why we prefer the rational numbers in the first place that give the subject it's name. Harking back to the last UHG video, since any natural number can be represented as the sum of at most four squares, are all conceivable rational quad-triples therefore representable in 4-d space but not necessarily in 3-d?

[@Hythloday71]

What / IS there a connection between Linearity as in straight line AND Linearity in Linear Algebra ?

[@billh17]

+Hythloday71 If you start at a given point on the straight line, then the rise is proportional to the run (that is, the rise is a linear function of the run). Algebraically, this is expressed as (y - b) = a * x, where y = ax + b is the equation of the straight line (with a and b constants).