# 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. ..

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

Constructions 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.

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

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

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.

One leaf like this each year. A less successful part of the jungle.

My flamboyan tree. Best year ever for flowers.

And here from underneath.

The monster plant. From 1 foot to 6 feet in 8 years, and prickly.

Ginger. Later the flower grows baby plants and more flowers.

Small apple bananas. Guineo manzano. Up to 300 on one stalk.

I don’t know the name of this one, but it is 6 feet high and growing.

Definitely not weed.

Voyager palm, it flowered three times this year.

A fancy bromelia.
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.