Funny Eggs.
This video looks at the differences between ovals and ellipses.
There is also an exciting experiment that tries to distinguish three eggs with different
physical behaviors.
From the background of this image, you can be sure that something will be said about
the Carolina Bays.
We start with the chicken and egg problem.
A chicken farmer has figured out that a hen and a half can lay an egg and a half in a
day and a half.
How many hens does the farmer need to produce one dozen eggs in six days?
You will learn the answer in due time, but first we discuss the differences between ovals
and ellipses.
The word OVAL describes the shape of an egg.
Sometimes it is used broadly to characterize an ellipse, but an oval does not have a precise
mathematical definition.
Do not let anyone tell you that ellipses are ovals.
Ellipses are geometrical figures described by a precise mathematical function.
Ellipses are conic sections produced by cutting a cone at an angle relative to its central
axis.
The angle of inclination of the cone can be deduced from the width-to-length ratio of
the ellipse.
An ellipse is a closed curve consisting of points whose distances from each of two fixed
points all add up to the same value.
In 1942, the book entitled The Origin of the Carolina Bays by Professor Douglas Johnson
proposed a hypothesis of complex origin for the Carolina Bays that included the flow of
artesian springs combined with wave and wind action.
Throughout the book, professor Johnson consistently describes the Carolina Bays as being oval,
as illustrated in his Figure 3.
However, the elliptical geometry of the bays can be verified easily even with the images
that professor Johnson had available when he wrote the book.
Each Carolina Bay has a different width-to-length ratio, but ellipses with the corresponding
ratios fit the outlines of the bays very well.
The idea that the Carolina Bays are ovals just lays an egg and makes it difficult to
explain the origin of the bays.
But by verifying that the Carolina Bays have elliptical geometry it is possible to deduce
that since ellipses are conic sections, the bays could have originated as inclined conical
cavities, and this can be demonstrated by oblique impact experiments.
This is a LiDAR image of the same bays described in Johnson's Figure 3.
The colors correspond to the topographic contours.
Comparison of these two images shows that the sand rims of the Carolina Bays are disappearing.
The image on the right from Johnson's 1942 book has broad, well-defined sandy rims, but
a contemporary satellite image on the left shows that the sandy rims have been reduced
to thin outlines during the past 78 years.
It would not be surprising if these bays were completely obliterated in a few centuries.
You can pause the video to check out the equations of how to solve the chicken and egg problem,
but the graphic makes it possible to get an intuitive answer.
The left part of the image shows a hen and a half producing an egg and a half in a day
and a half.
So in three days, a hen and a half will produce 3 eggs, and in six days a hen and a half will
produce 6 eggs.
All we need to do now is double the number of hens, so a hen and a half times two equals
3 hens, which will produce 12 eggs in six days.
We now come to an exciting experiment with ovals that shows that every egg has a surprise
inside.
We take the first egg on the left and we try to spin it.
The egg spins slowly and sometimes it does not spin well at all.
Now we are going to spin the egg in the middle.
This one spins very fast.
The third egg spins very chaotically.
It seems that the center of gravity is not where it should be.
It spins in a strange way.
When we shake the third egg it makes a rattling sound.
This egg has dried up and the yolk is loose inside.
We are cracking the second egg and removing the shell.
This is the egg that was spinning very well.
After removing the shell with some difficulty, we find out that this is a hard-boiled egg.
Now we crack the first egg, which is a raw egg.
This is the reason why it did not spin very well.
Our experiment showed us that a raw egg does not spin very well, whereas a hard-boiled
egg spins very well.
A dried egg is very light because all the water has evaporated and it spins irregularly.
If the yolk is loose, a dry egg will rattle when shaken.
As promised, here is the punch line: The joke is inside.
[buzzer] Sorry folks.
The yolk is inside.
Close enough.
The take home message is this: Do not confuse ovals and ellipses.
With ellipses you cannot make huevos rancheros.