Maths Work Out 1 – Think of a Number …

“Think of a Number” is a common starting point for maths problems that use algebra.  But you don’t need to know or use algebra to have fun with them.   So …
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The moon’s changes

So what can we notice if we watch the moon?

The first, most obvious, feature is that its shape changes, and then, if we watch it regularly, it soon becomes clear that it doesn’t appear in the sky at the same times each day.  After keeping an eye on it from time to time for a while, these changes are predictable.  At the time of writing (20th July 2012), the moon was what we call “new” the day before yesterday, so it’s not yet visible to my eyes, but I can imagine how it looks and where it is, a tiny thin sliver of a crescent, lost in the glare of the sun, trailing a little behind that brighter body as they both cross the sky from east to west.  As the sun sets tonight, I shall keep watch:  with the solar brilliance slipping below the horizon, I may just be able to discern the moon’s silvery line.  If not tonight, surely tomorrow I will see it (weather and cloud cover permitting).  A couple of days ago, the moon rose and set at pretty much the same time as the sun, although we couldn’t see it, lost as it was in the sun’s glare, but each day the moon lags behind by between a bit under an hour and a little over an hour and a half, depending on where it is in its cycle.  So each day for about the next ten days, the moon will be rising a bit later, further behind the sun, and will be appearing bigger and brighter in the sky.  By the time the moon is full, It will have got so far behind the sun that it will be rising about the time that the sun is setting, and setting around sunrise.  Funny, isn’t it, how we think of the moon as a feature of the night, when actually it can rise and set at any time of the day or night, including, at new moon, around the same time as the sun.

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Why I watch the moon

Following the seasons, noticing the shifts in the sun’s movements across the sky, being aware of the phases of the moon:  these were once core skills that helped our ancestors to survive.  Hunter-gathers used this knowledge to predict where they would find plentiful vegetation, or when to prepare to follow the herd that provided their meat.  Agricultural communities planted their crops according to the time of year, and needed to predict when to start preparing for the fallow months.  Most societies had stories about the cosmos, that helped them to explain the world and understand their place within it.  Each community had to devise their own calendar, incorporating the moments in the year’s cycle that were key to their existence, and to do this, they followed the movements of the sun and the moon.

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