hypotheses regarding human headshape and hat shapes

Hypotheses:

- human head shape, in a horizontal plane just above the ears, is
approximately the shape made by joining a semicircle with a
semi-ellipse, where the ellipse has eccentricity 1/sqrt(2)

- hat ovals are ellipses with eccentricity 0.5

I'd be grateful for any help with this.

Neil

--
Neil Fernandez

In article ,
Neil Fernandez wrote:
Hypotheses:

- human head shape, in a horizontal plane just above the ears, is
approximately the shape made by joining a semicircle with a
semi-ellipse, where the ellipse has eccentricity 1/sqrt(2)

- hat ovals are ellipses with eccentricity 0.5

I'd be grateful for any help with this.

It is not clear what you are asking. Short
answer is cause and effect. Hats are supposed
to stay on the head, thus a square hat will fly off
a round hole.

If your question is why are heads the shape they are,
I suggest you get pregnant and deliver the kid while
thinking about square heads with corners fitting through
a round hole. Committing this action will be safer than
asking a female who is in labor.

/BAH


Subtract a hundred and four for e-mail.

"Neil Fernandez" wrote in message
...
Hypotheses:

- human head shape, in a horizontal plane just above the ears, is
approximately the shape made by joining a semicircle with a
semi-ellipse, where the ellipse has eccentricity 1/sqrt(2)

- hat ovals are ellipses with eccentricity 0.5

I'd be grateful for any help with this.

Just what kind of help are you looking for?

-Michael.

Neil Fernandez wrote:
Hypotheses:

- human head shape, in a horizontal plane just above the ears, is
approximately the shape made by joining a semicircle with a
semi-ellipse, where the ellipse has eccentricity 1/sqrt(2)

- hat ovals are ellipses with eccentricity 0.5

I'd be grateful for any help with this.

Step one: start measuring hats and heads.
Step two: verify/debunk your hypotheses based on the data collected.

BTW, what is your hypotheses based on? What do you plan to do with the
results?

--
Will Twentyman
email: wtwentyman at copper dot net

In article , Michael
Jørgensen writes

"Neil Fernandez" wrote in message
...
Hypotheses:

- human head shape, in a horizontal plane just above the ears, is
approximately the shape made by joining a semicircle with a
semi-ellipse, where the ellipse has eccentricity 1/sqrt(2)

- hat ovals are ellipses with eccentricity 0.5

I'd be grateful for any help with this.

Just what kind of help are you looking for?

I was hoping to get some knowledge from others who have previously
thought about head shape, know about millinery, or can contribute to
discussing the hypotheses. Clearly I am not the first person to have
thought about these things. The cross-section of a human head appears to
be a nice geometrical shape, and surely of interest to some of those
maths heads who wonder at the shape of a Romanescu cauliflower or a
seashell. The constraints are presumably very simple, as they are for,
say, the pattern on a pineapple.

The semicircle/semiellipse_with_e=1/sqrt(2) hypothesis seems reasonable
as a first guess, and has probably been made before.

As for hat 'ovals' with e=0.5, well I was hoping for feedback from the
two rec.crafts.* groups.

Regards,

Neil

--
Neil Fernandez

Neil Fernandez wrote:
I was hoping to get some knowledge from others who have previously
thought about head shape, ...

While we're at it, I've often wondered how much a head weighs. How can I
weigh my own head? Seriously.

Bob H

There was a K-Mart commercial a few years back that claimed a human
head weighed eight pounds. The child who said the line didn't cite
sources; I assume that if the statement were true that eight pounds is
an average of various head weights (compiled by medical examiners of
decapitation victims, maybe?).

"Bob Harris" wrote in message
news:BE4BB9F5.48A72%plasticnitlion@wrappermindspri ng.com...
Neil Fernandez wrote:
I was hoping to get some knowledge from others who have previously
thought about head shape, ...

While we're at it, I've often wondered how much a head weighs. How can I
weigh my own head? Seriously.

Bob H

The standard method is based on the fact that the density of a head is
approximately the same as the density of water. Here's an outline of the
typical "Archimedean method":

1. Place a large bucket above an overflow pan.
2. Fill the bucket with water (either to the rim or to an overflow spout),
3. Stick your head into the water (up to whatever point on your neck that
you define as the end of your head)
4. Collect the overflowed water in the pan.
5. Measure the number of ounces of water collected.
6. The weight of the water will approximately match the weight of your
head.

Details (such as handling unwanted spills) are left to the user.

Carl G.

Neil Fernandez wrote:

I was hoping to get some knowledge from others who have previously
thought about head shape, ...


While we're at it, I've often wondered how much a head weighs. How can I
weigh my own head? Seriously.

Bob H

Take two pails/buckets of a size where your head will fit in the smaller
pail and the smaller pail will fit into the larger pail with room to spare.

Weigh the larger pail (empty) and note the weight then put the smaller
pail into it and fill the smaller pail to the 'brim' and no more.

Insert head into the water in the inner pail as vertically as possible
(head down) until the water just covers your chin (you may need a
'spotter' to confirm this).

Remove head from the water and allow excess water to drain back into the
smaller pail but ensuring no 'run off' gets into the larger pail.

Once the dripping has slowed enough wrap a towel around your head and
lift the small pail from the larger one and allow the water from the
outside of the small pail to drip into the larger pail.

When the drips have stopped weigh the larger pail (complete with
'caught' water) and subtract the empty weight from the 'new' weight. The
resulting figure should be the weight of your head (to within a
fraction of an ounce).

This principle is used to determine the weight of ships as a 'body'
placed in water will displace it's equivalent weight of water.

HTH,

--
Larry Green