history of mathematics - National STEM Centre

158
Hints
Activity 2.3, page 15
2 First exclude the two 'exceptional' numbers in the right-hand column.
3 What is a half in decimal notation, and in Babylonian?
Activity 2.5, page 17
3 Writing a fraction in sexagesimal notation is comparable with the following
decimal conversion.
10 10
Activity 2.11, page 24
= ~To — + i_ io~ = — To + -^ii " = A +4 = 0 . 25
10 io 2
rn 2 in in 2
2 x - y = 1 from line 1; -%(x — y) = \xl from lines 3 to 5.
Activity 3.2, page 32
4 b A median of a triangle is a straight line from one vertex of a triangle to the
mid-point of the opposite side.
Activity 3.3, page 34
1 g Draw an arc of a circle, with centre H and radius HI. Extend GH to intersect
this circle outside GH at N. Then GN is a line segment divided at H into lengths a
and b. Now you need to construct a right-angled triangle with hypotenuse GN. Use
the fact that all vertices C of the right-angled triangles ABC, of which AB is the
hypotenuse, form a semi-circle with diameter AB.
Activity 4.7, page 49
1 b Think about the coefficient of x in the parabola.
c Think about the difference between calculating QM given the ^-coordinates of A
and B, and finding the lengths UV and HK given the ^-coordinates of P, M, R.
Activity 4.9, page 50
1 b Notice that the section MPN is parallel to the base BCE of the cone, and so is
a circle. What does this tell you about the triangle MPN? How does this fact help
you to use the idea of a mean proportional?