Catenaries cannot be imagined without the existence of gravity (should I say space-deformations?). Architects are well-related with them for their usefulness in bridge construction, tall cathedrals, and decorative construction design.
The catenary is an interesting curve because being a curve formed by the influence of gravity, then catenaries do not exist as pure curves in plane geometry. This is an interesting fact since without going into spacetime-geometry or other space deforming forces, we have with catenaries an example in the pure Euclidean plane of how a curve can be generated with the influence of external factor to geometry and mathematics itself.
We think of countable sets as those with a finite quantity of elements. However, some infinite sets are also countable. Is this a paradox? Yes, finite sets are obviously countable. The set of all natural numbers between number 5 and number 10 is a finite set because it has only 4 elements; the numbers 6, 7, 8, and 9. We call this set a finitely countable set.
On the other hand, the set of all even numbers is infinite because there is no last even number. We have no way of imagining the biggest even number. The same can be said of the odd numbers, the prime numbers, so with many other infinite sets.
A parabola can be visualized as the plane curve traced by the locus of a point moving around a fixed point called the focus of the parabola and satisfying a predetermined parameter. From this standpoint of view, the parabola is a plane curve of the Cartesian plane. As such, the parabola belongs to the field of analytic geometry.
But the parabola can also be visualized as a section of a 3D solid body: the cone. As such, then the parabola is also called a conic section.
Parabolas are very similar in shape to catenaries, and because of their similarity, they are often confused.
The Moon has been the inspiration spot for poets, writers, novelists, painters, scientists, astronomers, physicists, preachers, etc.
So much fantasy has been woven around the Moon, that it is hard to believe some stories that are true, like the true fact that there are cremains of a human being on the surface of the Moon. Or the incredible story that there are here -on our planet Earth- some trees that are called "the Moon trees" because their seeds were taten to the Moon and back..
How hard is it to accept that 0.999... = 1? There are many ways to show that this equality is true. Mathematics is full of paradoxes. Paradoxes are apparent contradictions, flawed reasoning, illogical statements.
One of the popular "paradoxes" is the equality 0.999… = 1. This is because at first sight we "reason" in the following way: how can a never ending decimal be equal to a finitely expressed natural number?
Credit cards are sized with secret dimensions of width and height. Take one of your credit cards in your hands and slowly try to see and feel the similarity with the golden rectangle. The golden rectangle, also called the divine rectangle, has been long studied by mathematicians and artists for centuries. The golden rectangle proportions are used by painters, photographers, and decorators for framing portraits using the same proportions used in the Greek Parthenon.
The credit card proportions are well established and standardized. That's the reason why every type of wallet has special compartments to store the credit/debit cards.