Table of Contents
Close Packing ; Close Packing in Two Dimension ;
In close packing, the particles are arranged as closely as possible in a regular array. This can be done in two dimensions, as in a crystal, or in three dimensions, as in a solid. In two dimensions, the particles are arranged in a checkerboard pattern, with each particle touching four others. In three dimensions, the particles are arranged in a cubic pattern, with each particle touching twelve others.
Close Packing in One Dimension
Close packing in one dimension is the arrangement of spheres in a row so that they are touching each other. Each sphere is surrounded by six others. This is the most efficient way to pack spheres in a limited space.
Square Close Packing:
Square close packing is a type of close packing in which square shaped objects are packed together. In square close packing, the objects are packed together so that their sides are in contact with each other.
Three Dimensional Close Packing
In three-dimensional close packing, every atom is surrounded by six other atoms, forming a close-packed array. The atoms are arranged in a face-centered cubic (FCC) lattice. In this lattice, the centers of the faces of the cube are occupied by atoms, and the corners of the cube are empty.
Three-Dimensional Close Packing from Two-Dimensional Close-Packing in Crystals:
Hexagonal close packing
When two-dimensional close packing is applied to a crystal, the result is hexagonal close packing. In hexagonal close packing, each atom is surrounded by six other atoms at the vertices of a hexagon. This results in a more densely packed crystal with a higher packing density.
Three-dimensional Close Packing from Two-Dimensional Hexagonal Close-Packing in Crystals:
The hexagonal close-packing of spheres is the densest way to pack spheres in a three-dimensional space. If we take a two-dimensional slice of this packing, we get a hexagonal pattern. If we take a second two-dimensional slice of this packing, perpendicular to the first, we again get a hexagonal pattern.
If we keep taking two-dimensional slices of the packing, we will eventually get a three-dimensional close-packing of spheres. The close-packing will be in the form of a hexagonal prism, with the spheres at the vertices of the hexagons and the sides of the prism being layers of spheres.
Stacking the Second Layer Over the First Layer
Once the first layer is complete, the second layer can be placed over the first. The second layer is made up of two identical pieces.
To stack the second layer over the first, the first piece should be placed so that the long edge is facing the short edge of the first piece. The second piece should be placed so that the long edge is facing the short edge of the first piece, and the short edge is facing the long edge of the first piece.
By Stacking the Third Layer Over the Second Layer
Now that the third layer is complete, it can be stacked over the second layer.
Again, begin by placing the first dough ball in the center of the second dough ball.
Then, use your hands to press and stretch the dough out from the center.
Keep pressing and stretching until the dough is the same thickness all the way around.
Then, use your hands to press and stretch the dough out from the center.
Keep pressing and stretching until the dough is the same thickness all the way around.
Finally, use a rolling pin to roll the dough out into a thin disc.
Make sure to roll it out evenly in all directions.
Then, use a sharp knife to cut the dough into 8-10 equal-sized wedges.
Finally, use a sharp knife to cut the dough into 8-10 equal-sized wedges.
To assemble the pie, start by placing one wedge in the center of the plate.
Then, place the remaining wedges around the outside of the plate.
Finally, brush the top of the pie with melted butter.
Then, sprinkle with sugar and cinnamon.
Bake in a preheated oven for 15-20 minutes, or until the crust is golden brown.
To assemble the pie, start by placing one wedge in the center of the plate.
Then, place the remaining wedges around the outside
