A

# egg

An egg is the female gamete, germ cell, or ovum found in all animals and most plants. Popularly, the term is used to describe those animal eggs that are deposited by the female either before or after fertilization and develop outside the body, such as the eggs of reptiles or birds.

The egg is a single cell which develops into the embryo after fertilization by a single sperm cell or male gamete. In animals, it is formed in a primary sex organ or gonad called the ovary. In fish, reptiles, and birds there is a food store or yolk enclosed within its outer membrane. In angiosperm, the female reproductive organs form part of the flower. The egg cell is found within the ovules, which upon fertilization develop into the embryo and seed. See also pollination.

## The shape of eggs

Eggs, such as chicken eggs, are often described as being oval in shape, which is effectively tautological since "oval" comes from the Latin ovus for "egg." Strictly speaking, an oval is a flat two-dimensional curve, so it is more accurate to say that an egg is shaped like the surface of revolution of an oval.

In real life, eggs, like ovals, come in a variety of forms all of which can be loosely described as "like an ellipsoid but with one end more pointed than the other." Because eggs vary in shape, so too do their mathematical descriptions. Having said this, there are a variety of ways to approximate the shape of a hen's egg by modifying the equation of an ellipsoid, x2/a2 + y2/b2 + z2/c2 = 1, so as to introduce an asymmetry about the long (say, z-) axis. These involve multiplying z2/c2 by a suitable term, so that y becomes larger on the right side of the y-axis and smaller on the left side. For example, x2/a2 + y2/b2 + z2/c2 (1 - kx) = 1 gives a good egg. Other useful egg approximations come from surfaces of revolution of Cartesian ovals, Cassinian ovals, and sections through cones and cylinders.

In France, where tennis first became popular, a zero on the scoreboard looked like an egg and was called l'oeuf, which is French for "egg." When tennis was introduced in the United States, Americans pronounced it "love."

Why is a hen's, or other bird's, egg shaped as it is? Because it gives strength even though the eggshell is thin enough to allow the young bird to peck its way out when ready. To demonstrate this strength, trying balancing a pile of books on four half egg shells. It is even possible for a person's weight to be supported in this way.

## Hard-boiled or raw?

Another trick with eggs is to distinguish between a raw egg and a hard-boiled one without cracking them open to see which is which. To do this, lie both eggs on their sides on a table and spin them as you would a spinning top. With a bit of practice, the cooked egg will be made to rise up for a few seconds, while the raw one will remain on its side.

The physics of this odd behavior was finally cracked by two mathematicians, Keith Moffat of Cambridge University and Yutaka Shimomura of Keio University, who reported their findings in the journal Nature in 2002. They concluded that friction between the egg and the surface produces a gyroscopic effect, which causes some of the kinetic energy of the object to be translated into potential energy, raising its center of gravity (see also Tippee Top).

As the hardboiled egg spins, its curved surface causes it to touch the tabletop at only one point. The contact point changes and traces out a little circle. If the texture of the tabletop is just right – the effect won't happen if the table is either too slippery or too sticky – the egg will slide a bit as it spins. This sliding slightly slows the spinning motion, introducing a wobble into the spin of the egg. This in turn tilts the egg a little, raising one end off the table more than the other, at which point the gyroscopic effect kicks in and translates some of the kinetic energy of the spinning egg into potential energy, and raises its center of gravity in a seemingly paradoxical way. This effect is heightened by the fact that as the end of the egg rises, the egg draws in closer to the axis of spin, causing it to spin more quickly – just as figure-skaters can make themselves pirouette faster by raising their arms above their heads. If the egg isn't spun fast enough to start with – about 10 revolutions per second – there won't be enough energy available for the effect to occur.

Why doesn't the effect occur with a raw egg? Because the inside of the egg is runny and it lags behind the shell. This lag serves as a drag, which slows down the spin rate and dissipates the egg's kinetic energy. This in turn reduces the friction between the egg and tabletop, and means that not enough energy is available to be turned into potential energy to raise the egg's center of gravity. As well as solving the mystery of the balancing egg, Moffat also found time to write a limerick to commemorate the event:

Place a hard-boiled egg on a table,
And spin it as fast as you're able;
It will stand on one end
With vectorial blend
Of precession and spin that's quite stable.