Halloween

Compensation

Is competitive eating risky behavior. Obviously, yes; some people have
died choking on a hot dog. And stomach distension and rupture are real.

Then again, eating every day is risky too. We are in the midst of a planetary
obesity epidemic.

Let's just say a little indulgence which is compensated for can be okay.


👻😉

https://www.chowhound.com/food-news/53701/does-your-stomach-really-expand-if-you-eat-more/

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P Pie Recipe

This recipe belongs to humanity.

It was raining, and I decided to make a dessert that
would use up long-standing shelved ingredients. I had evaporated
milk on hand, and the below recipe is under the can label. So...

I did have some pumpkin puree, which I thawed. I didn't have
a pie shell, but I did have past due  flaky pastry in the freezer.
So... ( It thaws nicely in two hours!)

I didn't have brown sugar, but I had white, to which I added a splash
molasses...

I has cinnamon and nutmeg, but no ginger or cloves. So I added
some vanilla  and a few teaspoons of cocoa powder.

Didn't forget the eggs, and bit of flour. Cooked for the suggested one hour and
fifteen minutes.

Didn't have the patience to wait all evening for it cool; had some
lukewarm.

Yahoo! Pure comfort. Do make it with regular pastry though; this version
is a bit hard to chop with a knife. Although, from the point of view
of flavor, it really is awesome.

Great Show

Lyse invited me to visit the Lantern Festival exhibition at the
Botanical Gardens, where she worked last summer . Had a great time!!

The tradition of the lantern festival belongs in the Spring, the Chinese new year,
and has evolved over time. Families can go out at night again aided by lanterns;
children go into the street to solve the riddles of the lanterns...and adults let go of
old selves, and embrace renewal.

The color red is today a symbol of good luck. In the legend,  dragons - now
associated with the Emperor - were various forms of pestilence, fires, storms
and so forth an unhappy God might bring on his people.
In one variant, red lanterns and fireworks were meant to deceive the
vengeful God, who would think the city was already burning.

The lanterns have become ornate, some peeking out of the water in
animal form. The exhibits also presents  (with a witch in attendance) - decorated
pumpkins - a best of, from various schools - and these are of a remarkable variety
and inventiveness. Great show, children allowed even at night!!

 https://www.facebook.com/lyse.ross.96/media_set?set=a.1962505290673833.1073741830.100007431429506&type=3

Calc

From the time of Antiquity, there has been fascination with Pythagorean triplets
ie right angle triangles with whole number sides. The most famous of these is 3, 4, 5,
pictured below. It is unique, and no other triangle with these proportions can be
drawn but the actual values can be scaled; thus 6, 8, 10 plays out the same.

source: Wikipedia


Other triplets have been identified: 5, 12, 13 is one as well. But it will look quite
different, and will have a reduced area.

                                              *     *     *

But other triangular shapes are possible as well. What if I have three pieces of fencing
in the proportions 6, 7, 8. What would be the area of that triangle. Modern mathematics
has an answer for me, and it involves precalculated tables of trigonometric functions
(or, in my actual case, instantly calculated on a pocket calculator).

source: onlinemathlearning.com

                                                  Law of Sines

source: Wikipedia

 We thus have two angles; the third will be 57.9°. We have our figure.

Fun fact: the Law of Cosines, when published in France, is known as the théorème 
d'Al-Kashi, for the Persian mathematician(1380-1429) .
                             
                                              *     *     *

How to derive these famous laws. For the Law of Cosines, it's complicated.
The essential difficulty is labeling the 'random' triangle correctly. Once this is done,
basic algebra will do it.

Because we have created a right angle triangle, a can be considered a hypotenuse
whose actual length scales the cosine value of the C angle. The height of the triangle
becomes a sine function on that same angle...

source: Wikipedia

The Law of Sines is generally considered self-evident.

                            

Squish

If one accepts the circle as point of reference, then any triangle
within one half circle will have a right angle at its apex.
Indeed, one is creating a half box when the entire circle is considered.
We are just playing squishy boxes.

And if we assign our right angle 90 degrees, then any triangle will contain
180 (because any box has four).

The area of our right triangle will be one-half that of its box.

The maximal inscribed box we can create is a square.
Its area will be one-half that of an outer box.

Squaring both sides will yield two inner boxes; thus, the area
of the outer box.

In point of fact, the circle is an orientation mechanism. Side b approaches
the value of the diameter in a squishier triangle, and side a approaches 0.
The square of the sides will always be equal to that of the hypotenuse.