pythagoras and surd forms

students find the missing length, in a simplified surd form
and find patterns
to extend ...
and maybe prove their cojectures

this work arose from James Pearce (@Maths Pad James) finding some interesting surd form questions (these are: question (3) on sheet (i) and question (1) on sheet (ii))

spider on a cuboid

Henry Dudeney posed a slightly more complex version of this problem ('Spider and Fly') in an English newspaper (Weekly Dispatch) on 14th June 1903

“Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, at A, and a fly is on the opposite wall, 1 foot from the floor in the centre at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? ”

it later appeared in his collection, 'Canterbury Puzzles' in 1908

exact trigonometric values

a ppt is here

find a quick(er) way to do this question

3D trigonometry

exam-style questions

ratio and polygon angles

the idea for one of the two regular polygon questions comes from the AQA 8360 course
a powerpoint is here

students may or may not be provided with some information:

thanks to Wikipedia and László Németh for the sequence of regular polygons

fraction that is a triangle

this task is adapted from one by Tony Gardiner
a rectangle rather than square grid doesn't alter the problem but can make it (seem) a bit different...

similar to the triangles in a square post

and fraction that is a triangle

all 30ths from 7 to 14 inclusive can be drawn for this grid size

apart from the two indicated

dividing line segments in a ratio

each of the shorter line segments is one third of the way along the line segment

also thirds
find the missing coordinates















this work links with the task 'jumping' where the triangle is at the mid-points of each side