AboutAzeem Hussain Expertise I can answer virtually any kind of question dealing with of Math 536 and below, my forte being in parabolic functions and analytical geometry.
I'm currently learning Calculus I, and cannot answer questions that deal with subject matter more advanced than that.
Experience I am neither a professor nor a teacher of this subject. I am merely a student who is gifted at mathematics and enjoys being of service to his community. I frequently tutor people in math and the results are usually great.
Publications Reflections, Riverside School Board (2005, 2006)
Education/Credentials Diploma of Secondary Studies from Chambly Academy High School, and IBO-MYP certificate as well. My lowest mark on a high school math final was 97%, peaking at 99% in 2006 and 2007 (second-highest Math 436 mark in the province). Being a Quebecer, I am fluent in English and French and can respond to questions easily in both languages.
Awards and Honors Pascal Math Competition, School Champion(2007)
Question I know this:
To draw a 60 degree angle, fix compass on point A and draw an arc intersecting straight line at B. Then fix compass on B and without adjusting compass radius, draw another arc intersecting the first arc at say C. Join A C and the angle CAB is 60 degrees.
Fine. Now, to bisect this, we have to fix compass on point C, adjust radius roughly to more than half of arc CB and draw an arc. Repeat with compass fixed at B and draw an arc. Join A to the intersection of this set of arcs at say X and XAB equals 30 degrees.
My QUESTION:
What is the reasoning behind doing the final set of arcs roughly more than half whose intersection joined to A gives XAB equal 30 degrees.
I hope the question is not ridiculous.
ANSWER: Hi Somnath,
I don't quite follow the part about the actual bisection. To my understanding, it would not work.
The way to bisect, according to what I know is the following. Place the compass on point A (the vertex) and select a radius. It does not matter what this radius is, as long as you stick to it. Draw an arc so that it intersects lines AB and AC (call them AYB and AZC). Keeping the same radius, put the compass on point Z and make an arc. Do the same with point Y. Connect the intersection of the two final arcs, X, to the vertex, A. AX is the angle bisector.
Hope this helps,
Azeem
---------- FOLLOW-UP ----------
QUESTION: Dear Azeem,
I should have been clearer ---
I begin with a straight line say AD. Fix compass on A and draw an arc intersecting AD at say B. Then using the same radius, fix compass at B and draw another arc that intersects the first arc at say C. I join the intersect C to A and I now have an angle CAB equal to 60 degrees.
I get your point about using points Z and Y to draw two final arcs, and drawing an line from their intersection X to the vertex A.
Fine. I have a bisector.
WHAT I wanted to know is, whether there is any logic/ theorem behind this final step --- that the intersect of the two final arcs of random but equal measure (but roughly more than half the first arc or they won't intersect) when joined to the vertex will always give a line AX that is the bisector.
Sorry to bother you again.
Answer Hey Somnath,
These arcs of random but equal measure serve as reference points. What is needed to bisect an angle is to find the locus of points equidistant from both lines. By using arcs that are of the same length (regardless of what that length is, as long as intersection will occur), it is possible to find the "midpoint" of the two lines, i.e. the angle bisector.
