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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.
11 comments:
Can anyone help me find a starting point for number 1 on page 94? I know it has to do with congruence of triangles, but I'm not able to visualize it yet.
Steven, I started by proving traingle AQP is congruent to AGB. Since they are congruent, AB=AP. Then there is one more set of triangles you can prove congruent which will give you AP=BS. Hope this helps.
Could anyone help me with number 10 on page 82 and number 10 on page 83? I am at a loss at where to start.
Victoria, if you haven't already proved it start by drawing auxilery lines from F to B, C, and D. You know that angle ABF= angle AFB, and you can do the rest with congruence of triangles.
Can anyone help me with 9 on 83? I don't know where to start.
Virginia, triangles ADC and ABC are congruent by the hypotenuse leg theorem. Angle DAC=BAC. Then traingles ADO (o is the center point) =ABO. The rest is proved by two adjacent angles that are equal make a straight line.
I know we've proven that two triangles are congruent if they have two corresponding angles and one side, but do we know that they are congruent if they have two corresponding sides and one of the angles? (other than in a right triangle that is)
Can someone refresh my memory on how to draw a square?
Slaughter- i think you first make the perpendicular bisector of a line. then draw an arc with the point of the compass at the intersection to get 2 equal sides. then draw an arc of the same radius from each new intersection point. where those 2 intersect will be the 4th vertex of the square.
Thanks Virginia
sam, I don't think we have proven two sides and an angle make a case for congruence, unless in a right triangle.
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