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The School of Athens
Euclid, as imagined by Raphael in this detail from The School of Athens.
Jamshed Al-Kashi
Al-Kashi was one of the greatest mathematicians of the 15th century, calculating the sin(1*) correct to 16 decimal places.
Al-Beruni
The 11th century scientist and philosopher managed to estimate the radius of the earth using a very creative method that employed trigonometry.
10 comments:
For #9 on 191, could triangle ABC be an isosceles triangle? I think so, but just wanted to check...
On number 5, what does it mean by the projection of BC on AC?
Steven, I don't know if I would assusme the traingle is isoscels because the problem did not specifically say. Earlier problems have specified. Hope this helps.
For #3 on p. 190, what is meant when they ask "what can be said about the four points mentioned in question one?" Are they asking if they will all be equal or something else...
I'm not sure how to do 9 on 191 without assuming its isoceles- can anyone help me?
michael, i think it is the line you get by drawing perpendiculars from B and C to AC, if thats what you were asking.
Virginia, I don't know if this is the way it is supposed to be proven, but I looked at the quadrilateral AJHK.
To answer Victoria's question, I think it is just asking to document any observation regarding the four points in these two cases. Maybe they are the same point for some of them. See if you find anything special. One way to verify is to draw things out or even do some constructions.
I'm curious about Victoria's response to Virginia's question about number 9 on 191. What are J and K in your diagram?
Virginia, as for your question, I would sketch a good diagram, including the altitudes and then look at all the right-triangles formed within the triangle ABC. Then try and find all the angles that you possibly can for the triangles within.
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