About

worldslaziestbusker

Bio: Nouns - Australian, marine ecologist, caffeine fiend, musician, surfer, diver, atheist, photographer, busker. Adjectives - passionate, energetic, moody. Conjunctions - and, but, or.

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7 thoughts on “About

  1. Sue HALLIWELL

    Love Prelude, Cook and Birdie!!!
    I will have to do some research of my own
    To understand the early mathematicians
    work … arcs and degrees escape me
    But well done Matthew !!!!
    Looking forward to hearing more 🙂

    Reply
    1. worldslaziestbusker Post author

      Hi Sue
      Thanks for listening.
      I will try to draw a simple diagram of what Erasthothenes was up to. I think I understand it, but whether or not I can put it on a white board effectively will put that to the test. Watch this space.

      Reply
      1. worldslaziestbusker Post author

        Obelisk shadows

        Here goes.
        An obelisk directly under the sun casts no shadow (in Eratosthenes case, it was a well into which the sun shone vertically). If, at the same moment you know that the obelisk at one point has no shadow, you measure the shadow of an obelisk at another point, the degrees of arc the shadow of the second obelisk makes with a line running vertically to the centre of the Earth is equivalent to the degrees of arc distance between the two obelisks.
        If, one fine equinox, you had obelisks in a line running from one pole to the other, as that line passed astronomical noon, the shadows would, between them, cover the full range of possible degrees of arc in a half circle, the length of each shadow being a function of where an obelisk lay relative to the equator. At the poles, the shadows would make a right angle to a nominal line between the obelisk and the centre of the Earth, indicating the obelisk lay ninety degrees of latitude distant from the equatorial obelisk, which would cast no shadow, there being zero degrees difference between it and the incident light. If you knew the distance between the two obelisks, you would simply need to multiply that by the factor necessary to make the ninety degree difference into a full circle, in this case, four.

        When we discuss degrees of latitude we are denoting an angle relative to the datum set at the equator, as would be measured from the centre of the Earth. That we can’t be at the centre of the Earth to make the measurement, and that the Earth isn’t spherical, as the system appears to assume, just goes to show how clever geodeticians can be in establishing the models on which we base our navigation systems, territorial claims and geolocated phone apps.

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