prior knowledge topics Flashcards
natural numbers
N: 0, 1, 2, …
Integers
Z: …, -2, -1, 0, 1, 2, …
positive integers
Z+: 1, 2, 3, 4, …
rational numbers
Q: a/b (a,bєZ, b≠0)
finite decimal representation or infinite aperiodic decimal representation
irrational numbers
infinite aperiodic decimal representation (π, e, surds, …)
surd
= root, the result of which is irrational
real numbers
R = Q U irrational numbers
complex numbers
C: a+bi
(a-bi)(a+bi) = a2+b2
circumcircle
triangle inside a circle
circumcenter => perpendicular bisectors
inscribed circle
circle inside a triangle
incenter => angle bisectors
orthocenter
meeting of all altitudes
centroid
= meeting of medians
central and inscribed angle subtend the same angle ⇒
central angle = 2 x inscribed angle
Thales’ theorem
an inscribed angle, that subtends the diameter of a circle, is equal to 90°
circumference and area of a circle
C = 2πr
A = πr^2