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See Fox 209 for definitions:A(ADS) + A(BER) = A(APB)/4, because DS=ER =(PH3)/2, and AS + BR = a2 + q2 = AB/2A(ADM) + A(CFN) = A(APC)/4, by DM = FN = (PH1)/2 , c2+s2 =AC/2A(CFP) + A(BEQ) = A(BPC)/4, by FP = EQ = (PH2)/2, b2 + r2 = BC/2,A(APB)+A(APC)+A(BPC) = A(ABC),shaded area = A(ABC) - A(ABC)/4 = 3*A(ABC)/4.MIGUE.
Very neat!Thank you Migue.
The three kites at the corners tile a similar copy of the original ABC reduced to half, no matter what is the shape of ABC.
See Fox 209 for definitions:
ReplyDeleteA(ADS) + A(BER) = A(APB)/4, because DS=ER =(PH3)/2, and AS + BR = a2 + q2 = AB/2
A(ADM) + A(CFN) = A(APC)/4, by DM = FN = (PH1)/2 , c2+s2 =AC/2
A(CFP) + A(BEQ) = A(BPC)/4, by FP = EQ = (PH2)/2, b2 + r2 = BC/2,
A(APB)+A(APC)+A(BPC) = A(ABC),
shaded area = A(ABC) - A(ABC)/4 = 3*A(ABC)/4.
MIGUE.
Very neat!
ReplyDeleteThank you Migue.
The three kites at the corners tile a similar copy of the original ABC reduced to half, no matter what is the shape of ABC.
ReplyDelete