
English text at bottom.
バラの花弁が果たして正確に対数螺旋を描くのかどうかはよく分からないが、少なくともそれに近い形状でできており、極座標系 (r, θ) で
r = aebθ where a > 0.
と表現され、回転が拡大縮小と同意となる変形をもたらす点においても極めて美しい。渦巻銀河も、熱帯低気圧の雲も、ひまわりの種も、松ぼっくりも、どれも皆対数螺旋(のようなもの)で出来ている。ハンガリーの作曲家ベッラ・バルトークの作曲技法と言われる中心軸システムでもこの螺旋構造が出てくるが、音楽理論には明るくないのでよく分からない。
で、そんなことはどうでも良いわけである。甘い香りに包まれながら、ぼうっと眺めていれば十分なのだ。
There are several meanings in symmetry and typically, in mathematics, the quality of having two parts that match exactly, either when one half is like an image of the other half in a mirror (Cambridge Dictionary). It is called ‘reflectional symmetry’. One of other important definition is ‘rotational symmetry’ and the shape is exacly same when it rotates 90 degrees for instance. There’s another important idea called ’similarity (geometry)’ where you may find exactly same shape after scaling (enlarging). Interestingly, a shape of rose petals has a very special nature. When you rotating a flower head, you may find rotating means enlarging.
I don’t want to spend your time to explain those type of mathematical things but, anyway, my conclusion in Japanese text was, ‘roses are roses are roses’ then it is always beautiful.
Rose is always beautiful so it is the queen of flowers 👌
Absolutely!
☺️
Roses are roses, they never look anything but beautiful.
and this is not a part of logic but emotion.
Mother Nature – always the finest artist. Beautiful image.
That’s true. I just took it as a photo but nature tells a lot.
yup. roses are roses are roses. And a great choice for the challenge. Orangy/sherbet colored roses are my favorite. They remind me of the sunrise/set.
Agree. I also like the orange color, which has a softness like vanilla ice cream. Additionally, I am drawn to the spiral shape of petals.
A beautiful photo!
Thank you. A beautiful rose gave me a beautiful photo and lots of messages. What wonderful.