I found this little sandal on a windward beach on Green Turtle Cay – Abaco, Bahamas
We always think of things arriving on beaches by the sea, but just maybe they just might have descended from the heavens.
This parachute is crafted from Leonardo da Vinci’s concept.
Though credit for the invention of the first practical parachute usually goes to Sebastien Lenormand in 1783, Leonardo da Vinci actually conceived the parachute idea a few hundred years earlier.
Da Vinci made a sketch of the invention with this accompanying description: “If a man have a tent made of linen of which the apertures (openings) have all been stopped up, and it be twelve braccia (about 23 feet) across and twelve in depth, he will be able to throw himself down from any great height without suffering any injury.”
Perhaps the most distinct aspect of da Vinci’s parachute design was that the canopy was triangular rather than rounded, leading many to question whether it would actually have enough air resistance to float. And since da Vinci’s parachute was to be made with linen covering a wood frame, the hefty weight of the device also was viewed as an issue.
Like many of da Vinci’s ideas, the invention was never actually built or tested by Leonardo himself. But, in 2000, daredevil Adrian Nichols constructed a prototype based on da Vinci’s design and tested it. Despite skepticism from experts, da Vinci’s design worked as intended and Nichols even noted that it had a smoother ride than the modern parachute.
I thought the ‘ Pursuit Curve’ design for this piece would have been very intriguing to Da Vinci
A pursuit curve is the path an object takes when chasing another object. Such a path might result from a fox pursuing a rabbit or a missile seeking a moving target.
More formally, a pursuer must always head directly toward the pursued, and the pursuer’s speed must be proportional to or match that of the pursued. Plotting the lines of sight at regular intervals and tracing out the corresponding paths can produce fascinating patterns.
Pursuit curves can arise in a variety of situations and may involve more than one pursuer. Suppose that a person stands at each corner of a square traced out on the ground. Each person looks directly at the person to his or her left, then begins to walk toward that person. If all four people move at the same time and at the same constant speed, each person follows a spiral path toward the square’s center.
In the case of a square, it’s possible to mimic the resulting pattern by constructing a series of larger and larger right-angled triangles, starting with a square in the middle. Such an arrangement of triangles and squares can serve as the basis for a colorful, eye-catching quilt.
When three pursuers start at the corners of an equilateral triangle, they meet at a point in the middle of the triangle. This meeting spot is known as a Brocard point, named for French army officer Henri Brocard (1845–1922). In general, a triangle has two Brocard points. In the equilateral case, the two points coincide.
A Brocard point has the property that lines drawn from the vertices to the point are inclined at the same angle to each side of the triangle.
Interestingly, Brocard found the points now named for him in the course of studying the problem of three dogs chasing one another. Instead of focusing on what happens in an equilateral triangle with all three dogs moving at the same speed, he looked at a more general case involving triangles that are not equilateral. However, he still wanted the dogs to meet at the same time and at the same point (the Brocard point). This meant the dogs had to run at different speeds along their spiral paths. Moreover, there were two possible sets of spiral paths, one set for each Brocard point.
Interestingly, for paths converging to a Brocard point, the successively smaller triangles remain the same shape from one snapshot to the next. If the speeds were kept constant, the triangles would change shape in successive snapshots.
The rules for drawing pursuit curves and their variants can serve as recipes for creating artistic designs. Pursuit curves offer many artistic possibilities, says English educator and artist John Sharp. They also have links to some very high-level mathematics, he notes.
ALL of the lines used to create this design are straight
