I love sunflowers!

I have been growing them along the driveway of our house facing the south side of Jefferson Park.

The park is located on the west side of Cleveland between Lorain and Cooley avenues and, West 132nd and 133rd streets.

I have been growing them since my late wife and I moved here from New York City in 2001.

Sunflowers have also been featured in advanced lectures in Mathematics that I have given at Riverside School – a pre-K to 8 CMSD (Cleveland Metropolitan School District) school.

While the photographs are not representative of all of Cleveland’s sunflowers in the 2019 season – I have included

the ones I saw this year – all from the neighborhood (south of the park) and two from other areas.

 

 

The third and fourth photographs are from flowers grown outside apartment buildings on Cooley Avenue between West 133rd and 134th Streets. Cooley Avenue is on the south side of the park.

 

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The following three photographs are from plants grown along the driveway of our house. The driveway leads to a two-car garage – with no cars in the garage. Being through and through fprmer New Yorkers -- my late wife and I never owned a car.

The photographs were taken in the first week of September – before the squirrels mounted an attack (they do that every year), knocked the sunflowers to the ground and munched on the seeds.

 

The sunflowers literally followed the sun – facing east in the morning and then slowly turning around.

 

While the previous photographs show the sunflowers that bloomed this year, the following two photographs show sunflowers painted on the north abutment wall of the Father Begin Pedestrian Bridge crossing the RTA (Regional Transportation Authority) at the West 65th an Lorain stop on the Rapid (railroad) line. The sunflowers were painted as part of the beautification of Cleveland prior to the start of the 2016 Republican National Convention. The murals were painted by artists under the guidance of the LAND Studio – a non-profit developer of urban parks an public art.

The first photograph shows the mural as seen from the platform --- about 40-feet away. I had to walk up to the bridge to see the sunflowers in a close-up in the second photograph.

 

There is a lot of graffiti on RTA property and some of it has appeared on part if the mural – but fortunately not directly on the flowers.

 

The following discussion pertains to mathematical implications and practical applications resulting from the layout of sunflower seeds as taught to 8th grade students in an advanced math course at Riverside School -- a CMSD (Cleveland Metropolitan School District) preK-8 school where I am a volunteer teacher. This is my 15th year.

One would think that Nature would have laid out sunflower seeds in a simple fashion – like at the intersection of radial and circumferential lines.

Definitely Not!

The seeds have been laid out at the intersection of 21 clockwise and 34 anticlockwise spirals as shown in the following graphic.

In Mathematics -- both 21 and 34 are Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, … in which each successive number is the sum of the previous two) and the ratio of 34/21 = 1.618……… equals a number called the Golden Section, the Golden Ratio, the Golden Mean, or the Mean Proportional.

 

The following graphic shows a modern showerhead designed following the spiral pattern of the sunflower seeds.