Tag Archives: garden

A surprise parabola and more garden

Idly wondering about the tangents from a point to a circle I constructed the figure below. The point A is on a circle and can be moved round the circle. The chord CD then moves around. The interesting thing is to see the envelope of this chord as the point A is moved. ..

parabola surprise constructio

Circles and hyperbolas galore, but when the big circle passes through the centre of the smaller circle the envelope is the surprise parabola. The question is “How do I find the equation of such a parabola? Sensible choice of origin and axes is the first thing. the y-axis is best as the line joining the centres of the two circles. Then you need an equation for the line CD, with a suitable parameter. Then a little bit of calculus………..Nice one for calculus students

parabola surpriseConstructions done with my web based program. Try it yourself: GEOSTRUCT

And now for January in Puerto Rico. I don’t know the name of the pink and white flowering tree, but I do know that without my machete the whole garden would be infested with babies from the first one.

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This one below is a yellow eleconia, also spreading madly.

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And this is a cute little tree with probably poisonous berries.

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And what the hell have they done to the post editor. It only works in BOLD

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Filed under calculus, caribbean, envelope, geometry, high school, math, Uncategorized

A change from math – my garden in Puerto Rico

Ten years ago I came to Puerto Rico, to Mayaguez on the west coast, to a house with the usual vast expanse of nicely trimmed grass. Now I have the controlled jungle I always wanted. More time spent cutting things back or down than spent trying to get things to grow.
annual leaf
One leaf like this each year. A less successful part of the jungle.
flamboyan
My flamboyan tree. Best year ever for flowers.
flamboyan from below
And here from underneath.
monster plant
The monster plant. From 1 foot to 6 feet in 8 years, and prickly.
ginger1
Ginger. Later the flower grows baby plants and more flowers.
baby apple bananas
Small apple bananas. Guineo manzano. Up to 300 on one stalk.
name unknown by me
I don’t know the name of this one, but it is 6 feet high and growing.
not weed
Definitely not weed.
voyager palm 2
Voyager palm, it flowered three times this year.
fancy bromelia
A fancy bromelia.weird fern tree
This is a fern, tree sized, with its annual one foot high flower.

There’s more, but I have to go out and cut some strays.

I am quite sure that there is math growing here, waiting to be spotted.

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Filed under caribbean, Puerto Rico, retirado, tropical garden