A couple of weeks ago, I posted an #animation of a point on a circle generating a #cycloid.
If you turn the curve "upside down", you get the #BrachistochroneCurve. This curve provides the shortest travel time starting from one cusp to any other point on the curve for a ball rolling under uniform #gravity. It is always faster than the straight-line travel time.
Anyway, the #animation took a bit of thought as it requires a bit of #Mechanics, some #Integration and is made a bit more tricky as the curve is multi-valued and so you need to treat different branches separately. The #AnimatedGif was produce with #WxMaxima.
Nothing too remarkable about tonight’s #sunset. I just happen to like the three parallel #contrails. We live under two orthogonal #airways here, one running north-south and the other east-west. The latter is usually busier as it includes transatlantic air traffic.
Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic#curve with #period over the #circle's circumference and has #cusps whenever the point is in contact with the surface (the two sides of the curve are tangentially vertical at that point).
Today we travelled to the #CityOfBath, which is just over an hour away by train, making it suitable for a day trip. We cycled to our #RailwayStation and left our #bikes there. In #Bath, we only used pubic #buses and walked everywhere; we were lucky that although today had been planned well in advance, the weather was wonderful.
After a quick visit in the morning to the #UniversityOfBath, we spent most of our time wandering around the centre of the #city. The #RoyalCrescent has houses on its perimeter, curved in a #CircularArc, overlooking a park on the lower slopes.
The #RiverAvon flows through the city and here, you can see it and also one of the famous #bridges, called #PulteneyBridge, which has shops over the span.
There’s a nice walk along a stretch of the #river and here you can see the bridge from which the last #photograph was taken. I like the reflection of the river on the underside of the #arch.
It’s #spring and the #flowers are blooming, which means that #Bees have got a good supply of food. They particularly seem to like the small flowers of the #Cotoneaster plant in the front #garden and throughout a #SunnyDay, there are always several dozen on it.
I was on a walk the other day and came across a pile of #timber. I also happened to have my #camera with me and I liked the #GeometricPatterns and #Colours I saw.
If I'm going to interpret this, the natives of Taiwan survived as the primary people in what we know today as the Philippine archipelago. From the Philippines, they spread everywhere.
In other words, they're all #Filipino! ᜑᜑᜑᜑ 😹 (Or, native Taiwanese to be exact.)
It has been many months since I posted any #photographs of a #sunset, so here is this evening’s – the first full day of #spring. I like the mixture of #blue, with an area of #red, #orange and #yellow about the #Sun and the interesting shapes of the #clouds.