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Construction of Triangles (SAA etc.)

Discussion in 'Mathematics' started by brookes, Apr 24, 2011.

  1. Reading your post has made me realise that I make quite a deal about the proper(?) technique of constructions and just class the GCSE questions you describe as protractor work. For your other question I call a protractor a protractor and an angle measurer is the full 360, blue tool with the arm that the students break off. It doesn't really matter what I call them as many of my students call them compasses. I quite like the full angle measurer as it just seems a much more appropriate tool for measuring angles (what with the arm that actually *turns* as well as it going up to 360).
  2. Who is your audience?
    Pick up the November GCSE higher Edexcel Paper.
    "Copy the triangle in the space below, the base (AB) has been drawn for you" (or something similar
    There was no compass required..
    You pick up your 8p blue 'see through' tesco protractor...remember which way up it should go and
    then copy the size of the angle....draw the triangle and move on.
    Now, do a geomerty course in High School in the USA and you will have far more interest and specialist aproaches.
  3. mature_maths_trainee

    mature_maths_trainee New commenter

    Hi Betamale,
    My audience is 'just' KS3 and KS4 students in the UK, but that doesn't mean I just aim to teach them 'what they need for a GCSE exam'. I prefer to try to teach them what I think is worthwhile, and then point out to them afterwards the degree to which they will be examined on the topic in the way I've described.
    I like the tell the most able students, at least, the most accurate information I feel they can handle. If that means telling them that the term 'construction' is used somewhat differently by different communities of people, then fair enough. As with American/English trapezoids/trapezia, for example.
    But at the moment, I genuinely don't know whether 'construction' is deliberately 'mis-used' to include use of protractors, or whether its actually erroneous. Make sense?
  4. we had this conversation a while ago and those of us pedantic enough to go the distance agreed that a 'geometric construction' should involve only pencil, compasses and straight edge, and a group of more able kids will enjoy knowing the strict definition and harrumphing when a textbook or worksheet - or even a gcse paper - falls short of such high standards
    the world is full of words that are used inaccurately by wider communities - describing a cipher as a code for example - it's fun to tell top groups the correct usage, but it's not as vital as, say, one not being a prime number, and a top set can take a quick swing throught the fundamental theory of arithmetic to back up why this matters
    on the other hand, words do change their meaning - i heard someone quite shocking (i mean it was quite shocking they did it) use 'momentarily' to mean 'in a moment' the other day - can't remember who now, but they were english, educated and not young - and probably on the bbc - what would lord reith have thought!
  5. Karvol

    Karvol Occasional commenter

    I have never been a big fan of constructions ( autocad works perfectly well in my humble opinion ), but it is interesting as a tool to create shapes that are simply not possible using measurements.
  6. I don't know about 'communities' in relation to construction problems.
    The original notion of 'Geometric Construction', attributed to Oenopides, involves the use of a compass, unmarked straightedged ruler, and presumably a sharp pencil and rubber. So data involving prescribed lengths and angles are outside of the rules of the game. What can be constructed with these restrictions was established a long time ago, and no serious mathematician would get excited about it, let alone use such an Oenopidean construction.
    The whole subject of geometric constructibility is now mostly of historical interest. In that context, it did, through attempts to solve the three classical Greek construction problems, lead to an amazing amount of important modern mathemathics.
    I have no problem with the term 'construct' in the context of a GCSE question, as long as the rules of that particular game are stated within the question. In my mind, the term does not immediately conjure up an Oenopidean meaning.
    BTW: It is possible to geometrically construct any angle that is a multiple of 3 degrees, but because 20 degrees is not construcible neither is 1 degree.
  7. i suppose in a crowded ks3/4 syllabus, there is no room for 'fun'?
    i mix y5/6 gat maths and gat arts kids and they love this topic - it particular appeals to bright dyslexic kids - i suppose that goes with the architect leaning

  8. I'm all for 'fun' hands-on maths, so it is great that your gat kids love this topic. I suppose loci would have the same appeal. There are lots of curves with wonderful names: The Witch of Agnesi; The Cardioid; The Strophoid ...
    I think I was really responding to the OP's query about the 'community' of geometric constructors, There isn't one amongst mainstream mathematicians.

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