Good afternoon,
My name is Jesús and I'm developing a web application that consists of a calculator triangles (
http://triancal.esy.es (currently only works well in the Chrome browser) ) although I am not a mathematician based stubbornness ( paper, derive and Geogebra ) I managed to get a lot of formulas to calculate a triangle with the minimum number of data possible , maybe some is unpublished , and limits to be introduced only correct data.
I do not get the following formulas (note: I don't have t (area)):
- The minimum perimeter of any triangle ( abc) known heights corresponding to the sides a and b.
- The maximum height and minimum corresponding to the side b of any triangle ( abc) known the value of its perimeter and height corresponding to the side a.
Due to my limited math skills in calculating derived for finding maxima and minima do not get to find some formulas , which is why I write if I could help , formulas start missing me that although I managed to find two possible areas ( ty td ) of a triangle from two heights ( x , y) and the perimeter (p);
v1=(x*x*(y*y+p*p)+3*p*p*x*y+p*p*y*y)/((12*p*(x+y)))
v2=sqrt(abs(pow(x,4)*pow((y*y+p*p),2)+6*p*p*pow(x,3)*pow(y,3)+p*p*x*x*y*y*(2*y*y-p*p)+pow(p,4)*pow(y,4)))/((6*p*(x+y)))
v3=-asin((2*pow(x,6)*pow((y*y+p*p),3)+18*p*p*pow(x,5)*pow(y,3)*(y*y+p*p)+3*p*p*pow(x,4)*y*y*(2*pow(y,4)+10*p*p*y*y-pow(p,4))+18*pow(p,4)*pow(x,3)*pow(y,5)+3*pow(p,4)*x*x*pow(y,4)*(2*y*y-p*p)+2*pow(p,6)*pow(y,6))/((2*pow(abs((pow(x,4)*pow((y*y+p*p),2)+6*p*p*pow(x,3)*pow(y,3)+p*p*x*x*y*y*(2*y*y-p*p)+pow(p,4)*pow(y,4))),(3/(2))))))/(3)
t1=v1-v2*sin(A60+v3)
t2=v1+v2*sin(v3)
Notes:
A60 = 60º angle in radians value is 1.0471975511965976
pow = high, example: pow ( ( x + y) , 4 ) is ( x + y) ^ 4
sqrt = square root
asin = arcsine
abs = absolute value
v1 , v2 and v3 = auxiliary variables
"I´m from Madrid (Spain) my english is low and i use google translator for this mail, sorry."
A greeting.
Jesús SD jsdcorreo@gmail.com