August 20, 2017 - Math Circle 2.0

Warm Up

Welcome back to Math Circle.   Let's discuss the solar eclipse that will happen Monday, August 21, 2017 in the USA.


Pinhole Camera

Safety first!  Never look at the sun directly without ISO 12312-2 compliant solar glasses.  You may look at the sun indirectly by making a pinhole camera.

Follow the link below to get the directions.

https://eclipse2017.nasa.gov/sites/default/files/EclipseCerealBoxViewer.pdf


Size of Sun, Earth, and Moon

The following link has a summary of the sizes and distances of the sun, earth, and moon.

http://blair.pha.jhu.edu/scale.html

Almost four diameters of the moon span the earth.
109 diameters of the earth span the sun.

The distance from the earth to the moon is 110 moon diameters
The distance from the earth to the sun is 11759 earth diameters

What does that look like?
How can we create a model of this?
What is a diameter anyway?

Scale - 1 earth diameter = 1 inch
distance from earth to moon is 30 inches
distance from earth to sun is 11759 inches, or 980 feet, or distance to the top of right of the rectangle formed by the sidewalks north of Foellinger auditorium.

aug 20

...2857142857142857143x7=?

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Quadrangles - what is the taxonomy:

Kites (pairs of neighboring sides equal) - Parallelograms (opposite sides <=> opposite angles are equal)-Trapezoids (pairs of neighboring angles are equal)

Rhombi (=diamonds)   Rectangles

Squares

Midsides operations: take midpoint of all 4 sides of a quadrangle Q, get another quadrangle M(Q).

Turns out, - M(Q) is always a parallelogram!

Q-rhombus <=> M(Q) - rectangle, and vice versa.

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Logics:

Two villages (Knights and Knaves), a person at the fork - which road goes to Knights village?

Larry, Leon, Tom, L's are liars, Tom tells truth. How to find if you speak to Larry?

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When the angle between the hands is wider: 5 past 11, or 10 past noon?
$x^2 $