1. Good evening(?) all,

My name is Samuel & I am from the UK.

Here we have allotments in which you rent out a space to grow your own fresh vegetables & fruit.

Ever since realising how I can apply science & maths to real life applications (in this case growing my own grub) my interest in these subjects has shot up (I only wish this spark would have came at the time I was in school!).

So I wish to grow the most fresh food I can on my plot and I have a couple of ideas/queries which I would like some advice/thoughts on (related to maths of course!).

OK so the name of the game here is to utilise all the space on my plot (both horizontally & vertically) to grow as much as I can.

The first thing that interests me is the Fibonacci sequence - which I believe is a mathematical sequence of numbers in which relates somewhat to nature & how/where plants 'position' their leaves to get the maximum sun light as they can? Now imagine growing lettuce vertically (here each lettuce plant is equivalent to a plants leaf), putting soil within a pipe and drilling holes at positions which mimic the Fibonacci sequence. Then planting young lettuce plants from the bottom with the newest planted at the top. What I am trying to do here is mimicking nature and the rules of maths she plays by and grow as much lettuce as I can (out of reach of the slugs!) with each individual plant getting as much light as it can. What does everyone think, will it work?

Secondly, something that interested me was growing on large mounds (for ease of visualisation let say the mounds are semi-circular shaped) as opposed to a flat ground as growing this way creates more surface area for which to plant vegetables (how can one determine how much more surface area for growing is created?). I was just wondering, with regards to geometry, how can I construct soil containing structures of which have the largest surface area for growing edible crops?

Samuel

p.s sorry for the long post

2.

3. As to say, what geometric shapes would provide the largest growing surface area?

Many thanks,

Samuel

4. Unfortunately, you have to take in to account the fact that soil will settle if the slope is too great. Most of the time, a mound of soil will settle into a roughly conical shape (which is why mountains are the shape they are). To begin with, you might can restrict yourself to finding the ideal cone taking in to account a variety of factors. You mentioned sunlight, but there's also water and the fact that plants like to be spread out a bit.

5. You could try some of the square foot gardening ideas.
Square foot gardening - Wikipedia, the free encyclopedia

I would recommend not buyiing any books if you can research the internet or borrow from a library.
I would recommend getting to know the other gardeners and possibly joining, or at least visiting, the local horticultural society.

One problem I have seen with people trying to maximize their planting is sometimes they crowd the plants too much which leads to stunted plants and turns out to be counterproductive. Plants usually need just as much area for their roots as they do for their tops, if not more. Overcrowded plants are stressed and usually end up small tough and bitter, like people who are raised in poor overcrowded conditions tend to do.

6. What benefits do you think a larger growing surface will provide? If you have a given area of (flat) space it will receive a certain amount of sunlight. Changing the shape will only result in some parts getting more and some less of that sunlight. Of course, if you go up high enough, you might be able to shade your neighbor's plot and steal some of his sunlight.

7. Some plants prefer partial shade to full sunlight, so that's something else to optimize.

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