Can you stack 4 spheres?

The answer is "yes": if you "stack" spheres on top of each other so that their centers are on the same vertical line, they will not fall down.

What is the maximum packing of spheres?

Experiments and computer simulations have shown that the most compact way to pack hard perfect same-size spheres randomly gives a maximum volume fraction of about 64%, i.e., approximately 64% of the volume of a container is occupied by the spheres.

How tightly can you pack spheres?

Recent research predicts analytically that it cannot exceed a density limit of 63.4% This situation is unlike the case of one or two dimensions, where compressing a collection of 1-dimensional or 2-dimensional spheres (that is, line segments or circles) will yield a regular packing.

How many spheres can simultaneously touch another sphere of the same size?

According to one telling of the tale, Newton held that a central sphere could touch no more than 12 surrounding spheres of the same size, but Gregory thought there might be room for a 13th halo sphere.

What is the sphere kissing problem?

The “kissing number problem” is a basic geo- metric problem that got its name from billiards: two balls “kiss” if they touch. The kissing number prob- lem asks how many blue balls can touch one given red ball at the same time if all the balls have the same size.

The Best Way to Pack Spheres - Numberphile

What is the kissing number in 3d?

The kissing number k(3) is the maximal number of equal size nonoverlapping spheres in three dimensions that can touch another sphere of the same size. This number was the subject of a famous discussion between Isaac Newton and David Gregory in 1694.

How many spheres can fill a cylinder?

There can be five sphere can be made from cylinder.

Is a sphere or cube stronger?

The arc (think: circle) is the strongest structural shape, and in nature, the sphere is the strongest 3-d shape. The reason being is that stress is distributed equally along the arc instead of concentrating at any one point.

What is the best shape to cover a sphere?

A triangle of foil is a good shape for wrapping a round candy or gift. The blue areas show the parts of the foil that come into direct contact with the sphere, while the yellow areas are wasted space. For your own purposes, the triangle method may be the most efficient, and the rectangle method is probably the easiest.

Why are spheres rarely used for packing?

Not only are they easily squashed, they also have shapes that don't lend themselves to being packed in boxes. Even the simplest possible fruit shape, the sphere as seen in oranges and apples, causes a problem, because no matter how you pack spheres, there'll always be gaps between them.

What is the rule of sphere?

The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter.

When each sphere is in contact with four other spheres?

The arrangement in which each sphere is in contact with four other spheres is called square close packing. The arrangement in which each sphere is in contact with six other spheres is called hexagonal close packing. In such a packing, the spheres of the third row are aligned with the first row.

What is the closest packing of spheres porosity?

The packing structure for spherical particles is the most well studied and well under- stood of these systems. The minimum bulk porosity of sphere packings is 0.36 (for uniform-sized spheres), and the values for real packings typically fall into the range e = 0.36-0.42.

What is the maximum size sphere in cube?

So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube. Therefore, the volume of the largest sphere inside the given cube is 36 π .

Which Hypersphere packing is densest?

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice is the densest of all possible plane packings (Conway and Sloane 1993, pp.

What is the strongest shape in the world?

Therefore, triangles are the strongest shape. This idea is supported by research and real uses of triangles in construction and design. I learned that triangles are the most rigid shape because forces on a triangle are distributed evenly along its three sides.

What is the most structurally sound shape?

The circle is considered one of the strongest shapes because stress is evenly distributed along the arc instead of concentrating it at one point.

What shape can hold the most weight?

The shape of an object or structure can affect its properties. As you saw, even though the paper columns are made of the same material, they have different levels of strength because they are different shapes. The cylinder can support the most weight—in this case from books—because its walls don't have any corners.

Are spheres faster than cylinders?

Objects of equal mass and radius but different shape or solid/hollow will roll down the incline at different rates. Solid sphere is faster than solid cylinder since sphere has lower moment of inertia, higher translational kinetic energy.

Can both a sphere and a cylinder roll?

A solid sphere and a solid cylinder, each having the same mass and radius, are released together at the top of an inclined plane and roll without slipping but also with negligible rolling friction.

How many cones fill a sphere?

To work out the are of a sphere remember its 2 cones.

What is the hardest question in math?

Goldbach's Conjecture

Goldbach's Conjecture is, “Every even number (greater than two) is the sum of two primes.” You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19. Computers have checked the Conjecture for numbers up to some magnitude.

What does 3 kisses mean from a girl?

Usually, one x (one kiss) is used for friends, two xx (two kisses) for best friends or close friends, and three xxx or more (three kisses or more) for your partner or super close friends.

What is a kiss in math?

In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere.