and one more point…since we can wrap any shape in a square there is always going to be a (line segment)^2 in the area…
one more observation…for a circle, if we find the best enclosing square, the total area of that square is 4*(radius^2)…but the actual area has to be lesser than this…so we have pi instead of 4.but can you tell me how this pi was reached??
darn you, Kalid! i’m in 3rd year calculus, but now all I want to do is go back to geometry again!
seriously, thanks for putting this up. this makes math fun again.
@Anonymous: Awesome, glad it helped! Yeah, it’s so easy to get distracted when math becomes enjoyable again :).
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**** this
[…] Here's an illustration, with credit going to (and further explanation found at) the site http://betterexplained.com/artic… Note that the blue triangle's top-left angle makes it similar to the green triangle, and […]
[…] continued, reading an article on the Pythagorean theorem, looking for something to rip apart. On finishing, I felt a deflated. It […]
For those of you that wonders if if maths are useful. Understandig Pythagoras helped me building my home. How to make 90 degrees corners in a house? Knowing Pythagoras says that marking 3 feets from the corner of one wall and 4 feets of the adjacent wall and then using the marks adjusting the sides till you get your 5 feet diagonal and voila… the sides forms a perfect 90 degree angle.
@Eyvind: That’s a great example of going backwards – yes, you can make a perfect right angle at home by making a triangle of sides 3-4-5!
Wow those are great examples. I found some other site that actually has circle, triangle, rectangle, and many other calculators.
http://www.thexorb.com/Algebra/Pythagorean/Pythagorean-Theorem-Calculation.aspx
I was confused by the Area Factor bit as well. So I did a little formulating.
Starting with: Area = F * hypotenuse^2
Replace Area: 1/2 Base * Height = F * hypotenuse^2
Rearrange: (Base * Height) / (2 * hypotenuse^2) = F
There is your area factor.
Making this useful, if you only knew you had two similar triangles with hypotenuses 3 and 4 respectively (as in the example) simply go back to Pythagoreas and solve for the missing hypotenuse of the combined triangles, knowing of course that the respective smaller hypotenuses become the sides of the larger triangle.
As Kalid said the Area Factor doesn’t really matter, but I still wanted to find a formula for it…voila.
vision sort of locked 3d sighting “Topologie ia branche mat who you presenting ability see it plus de sides is the key of a triangles example bending Arcsin(x):
sides is statement the many mat formats
krob
Brilliant. Exactly what I was looking for.
this was so interesting…
can’t be better than this
Thanks. Your explanations on the physic were brilliant. It must surely also applies to others like the mgh,pVg(buoyant force),hpg(pressure) and others.
thanx