Heron's Formula Exploration

Expression 12: "f" Subscript, "a" "r" "e" "a" "W" "i" "t" "h" "H" "e" "r" "o" "n" "s" "F" "o" "r" "m" "u" "l" "a" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis equals "f" Subscript, "w" "r" "a" "p" "p" "e" "r" , Baseline left parenthesis, distance left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , right parenthesis , distance left parenthesis, "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis , distance left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis , right parenthesis

Expression 13: "f" Subscript, "a" "r" "e" "a" "W" "i" "t" "h" "B" "a" "s" "e" "H" "e" "i" "g" "h" "t" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis equals "f" Subscript, "B" "a" "s" "e" "H" "e" "i" "g" "h" "t" "D" "r" "i" "v" "e" "r" , Baseline left parenthesis, distance left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , right parenthesis , "f" Subscript, "g" "e" "t" "H" "e" "i" "g" "h" "t" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis , right parenthesis

Expression 14: "f" Subscript, "B" "a" "s" "e" "H" "e" "i" "g" "h" "t" "D" "r" "i" "v" "e" "r" , Baseline left parenthesis, "b" , "h" , right parenthesis equals StartFraction, "b" "h" Over 2 , EndFraction

Expression 15: "f" Subscript, "v" "e" "c" "t" "o" "r" "i" "z" "e" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , right parenthesis equals left bracket, "p" Subscript, 2 , Baseline . "x" minus "p" Subscript, 1 , Baseline . "x" , "p" Subscript, 2 , Baseline . "y" minus "p" Subscript, 1 , Baseline . "y" , right bracket

Expression 16: "f" Subscript, "g" "e" "t" "T" "h" "e" "t" "a" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis equals arc cosine left parenthesis, "f" Subscript, "C" "o" "s" "S" "i" "m" , Baseline left parenthesis, "f" Subscript, "v" "e" "c" "t" "o" "r" "i" "z" "e" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , right parenthesis , "f" Subscript, "v" "e" "c" "t" "o" "r" "i" "z" "e" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis , right parenthesis , right parenthesis

Expression 17: "f" Subscript, "g" "e" "t" "H" "e" "i" "g" "h" "t" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis equals distance left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis sine left parenthesis, "f" Subscript, "g" "e" "t" "T" "h" "e" "t" "a" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , "p" Subscript, 3 , Baseline , right parenthesis , right parenthesis

Expression 18: "f" Subscript, "g" "e" "t" "T" "h" "e" "t" "a" , Baseline left parenthesis, "P" Subscript, 1 , Baseline , "P" Subscript, 2 , Baseline , "P" Subscript, 3 , Baseline , right parenthesis equals 66.8 9 6 6 3 7 8 4 1 1

equals

66.8 9 6 6 3 7 8 4 1 1

Expression 19: "f" Subscript, "m" "a" "g" , Baseline left parenthesis, "f" Subscript, "v" "e" "c" "t" "o" "r" "i" "z" "e" , Baseline left parenthesis, "P" Subscript, 1 , Baseline , "P" Subscript, 3 , Baseline , right parenthesis , right parenthesis

equals

0.9 4 8 0 3 3 7 5 4 6 7 3

Expression 20: "f" Subscript, "m" "a" "g" , Baseline left parenthesis, "v" , right parenthesis equals StartRoot, "v" left bracket, 1 , right bracket squared plus "v" left bracket, 2 , right bracket squared , EndRoot

Expression 21: "f" Subscript, "d" "o" "t" "P" "r" "o" "d" "u" "c" "t" , Baseline left parenthesis, "v" Subscript, 1 , Baseline , "v" Subscript, 2 , Baseline , right parenthesis equals Start sum from "i" equals 1 to length left parenthesis, "v" Subscript, 1 , Baseline , right parenthesis , end sum, "v" Subscript, 1 , Baseline left bracket, "i" , right bracket times "v" Subscript, 2 , Baseline left bracket, "i" , right bracket

Expression 22: "f" Subscript, "C" "o" "s" "S" "i" "m" , Baseline left parenthesis, "v" Subscript, 1 , Baseline , "v" Subscript, 2 , Baseline , right parenthesis equals StartFraction, "f" Subscript, "d" "o" "t" "P" "r" "o" "d" "u" "c" "t" , Baseline left parenthesis, "v" Subscript, 1 , Baseline , "v" Subscript, 2 , Baseline , right parenthesis Over "f" Subscript, "m" "a" "g" , Baseline left parenthesis, "v" Subscript, 1 , Baseline , right parenthesis times "f" Subscript, "m" "a" "g" , Baseline left parenthesis, "v" Subscript, 2 , Baseline , right parenthesis , EndFraction

Generate a triangle

References: