Equator!!

Q: The circumference of the Earth is approximately 40,000 km. If we take a wire that is only 10 meters (0.01 km) longer than the circumference of the globe and circle it around the globe, can a flea, a mouse, or even a man can creep under it?

Solution

Circumference = 2*PI*r

Radius of Earth, rE = 40000/2*PI = 6366.1977236758134307553505349006

Radius of Wire, rW = 40000.01/2*PI = 6366.1993152252443497087082237382

Difference is 0.0015915494309189533576888382082065 = approx 1.6 m

So a tall man must duck to go through it but a smaller man can easily go through.

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Corner to Learn@:

Actual Circumference of the Earth is:

At the equator: 24901 miles
Around the poles: 24859 miles
[This is because the spinning of the earth creates a bulge.]

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8x8 Grid

Q: A 2x2 grid can be achieved by drawing three squares on a sheet. How many squares (in minimum) are needed to get a 8x8 grid?


Solution: 15

How? [(0,0) (8,8)][(0,0) (7,7)][(0,0) (6,6)][(0,0) (5,5)][(0,0) (4,4)][(0,0) (3,3)][(0,0) (2,2)][(0,0) (1,1)][(1,1) (8,8)][(2,2) (8,8)][(3,3) (8,8)][(4,4) (8,8)][(5,5) (8,8)][(6,6) (8,8)][(7,7) (8,8)]