Sir Mike Ambrose is the author of the question.
Showing that brown area ÷ smaller octagon area = a/b.
Let the side length of the smaller regular octagon be 1 units.
a = ⅛*180(8-2)
a = 135...
Sir Mike Ambrose is the author of the question.
Calculating the exact hatched area.
Let x be the radius of the inscribed circle.
2x² = a²
a = √(2)x cm.
b = x+a
b = (x+√(2)x) cm.
c =...
Calculating Shaded Area (Trapezoid).
It implies;
½ ~ 1
½√(3) ~ x.
Where x is the base of the blue shaded trapezium.
Cross multiply.
½(x) = ½(√(3))
Therefore x = √(3) units.
T...
Calculating Length x.
a = 180-45
a = 135°
Length x is;
x² = (½*5√(2))²+(½*7)²-(½*5√(2)*½*7*2cos135
x = √(½*25+¼*49-½*35√(2)cos135)
x = √((50+49-70√(2)cos135)/4)
x = ½√(99-70√(2)c...
John Horton Conway (b1937)
The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a gam...
Kindly move the question right/left one time to review the framework/analysis.
Thank you nicely.
Calculating area circle.
Let the radius of the circle be r.
r²=2²+(r-1)²
r²=4+r²-2r+1...
Calculating x, radius of the big inscribed green circle.
Radius, r of the bigger inscribed red circle is;
2(1-r)²=(2r)²
r²+2r-1=0
r = (√(2)-1) units.
Therefore radius, x of the big i...
Fruity Numbers Adventure.
In the sunny orchard, Anna finds a talking apple tree.
The apple tree says, 'Let's count my apples together! How many can you see?'
Anna counts, 'One, two, three,' and...
Paul Erdös (1913-1996).
Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to...
Calculating Area Green.
Let z be the width of the ascribed rectangle.
Let y be the length of the ascribed rectangle.
½(az) = 22
a = 44/z cm.
½(by) = 48
b = 96/y cm.
c = y-44/z
c =...
