What it takes to be a giant

On a walk around the San Jose neighborhood, I encountered a single absolutely giant sunflower in a sidewalk garden.

giant sunflower

I admired the size of the flower head, which was about 16 inches across and probably weighed 10 pounds, wondering how many seeds must be packed in so very tightly and mathematically precisely (see an earlier post on “how many seeds in a sunflower seed head?”).

giant sunflower

Seeds are precisely arranged in spiral rows to maximize packing.

But then I got to thinking about what it takes to produce that giant flower head and develop all those seeds.  Supported by enhanced woody fibers in the stalk and fed by photosynthetic machinery in huge, oversized leaves and an elongated, deep taproot reaching deep into the soil for water and nutrients, the enormous reproductive output of this plant has the potential to be record-breaking.

But alas, a quick google search confirmed that Hans-Peter Schaffer holds the Guinness record for sunflower height (30 feet, 1 inch), mine was probably just over 8 feet. The giant Mongolian sunflowers routinely grow to 16-18 feet and sport 18-24 inch flower disks, so my giant wasn’t really record breaking at all.  Still impressive for an herbaceous plant, though!

How many seeds in a sunflower seed head?

I planted giant sunflowers in the back of the vegetable garden this year, just on a whim to see if I could provide some “natural” food for the birds.  The plants did indeed become gigantic — more than 12 feet tall (see Sept 2 post).   The flowers were about 8 inches across, and attracted a variety of pollinators, but were most attractive to the bumblebees (one is working on the giant sunflower below).

Unfortunately, it wasn’t the birds who discovered the maturing seed heads, it was the squirrels, who were climbing the stalks and pulling the flowers over and eating them.  So, I had to harvest the flower heads a little early, before the seeds in the center had a chance to mature.  Even though slightly immature, these seed heads were enormous (compare with camera lens cover).  You can see the squirrel damage on the flower on the left.

Some of the disk flowers had not dropped off yet, but there were maturing seeds underneath.  These flowers are a testament to the pollination efficiency of those bees, as illustrated below (with disk flowers removed).  If there ever were a demonstration of the eco-service provided by bees, this has to be it.  It looks like almost every single one of those disk flowers got pollinated and fertilized and has at least tried (less successfully in the center) to produce a seed.

You can see the beautiful geometric pattern of spirals that promotes the most efficient seed packing into limited space (read about the “golden angle” in the post on Sept 2).  But just to drive the point home, here’s a close-up.

So you can better appreciate the geometric spiralling pattern, I drew on the seed head to help me keep track while counting seeds.  Yes, counting the seeds, because I wanted to know how many seeds were in a 6.25 inch diameter sunflower seed head.

Now, here’s the interactive part of this post.

How many seeds do you think there were in this seed head?

Sunflower math

A golden rule of biology is that individuals attempt to leave as many offspring (i.e., genes) as possible in the next generation.  Plants, like the sunflowers growing in my backyard right now, try to maximize their seed production by packing seeds into the flower head in the most optimal way.  And that’s where the math comes in.

The sunflowers have grown quite tall (the fence posts are five feet), and some of the flowers are dinner-plate size (that’s a bumblebee on the flower head below for size reference).

But have you ever really inspected the interior of one of these complex flower heads?

The outer, yellow petals are really individual infertile ray flowers.  The center, disk flowers open from outer toward inner rows, a few layers at a time.  The yellow-tipped anthers stick up from the central part of each flower, presenting a disk of pollen for the lucky pollinators.

Once fertilized by the many bees that visit these flowers, each of the individual flowers produces one seed.  The entire flower head can produce as many seeds as there are individual disk flowers.  So the question is, how to pack as many of those flowers as possible into the circular head.

This pattern is not random.  Each disk flower (or potential seed) lies at an angle of 137.5 degrees from its neighbor.  Lined up from center to outer rim, the flowers (or seeds) describe two sets of spirals, one curving to the left, and one curving to the right.  This is the formula for maximal packing into circular space, and has been termed the “golden angle”.

As explained by mathematicians, divide a circle into two sections, such that the ratio of the large arc to the small arc is the same as the ratio of the entire circle to the large arc.  The golden angle is that created by the smaller of the two arcs, exactly 137.5 degrees.


Applying the golden angle to the construction of the flowerhead, we get the following sort of pattern.

Pretty darn smart of those plants!

A crop of sunflowers growing in northwestern Minnesota near Crookston.