cone frustum

how do you work out the volume (in general)?
[it's a cone with a smaller cone chopped off]

how do you work out the curved surface area?
[it's a part of an annulus]

what if you don't know 'h' ?

find the volume of the cup

what is the volume of this bowl?

work out the dimensions of the portion of the annulus (washer shape) needed to make the fabric of this lampshade

(ignoring any overlap of material)

show that the angle required is 207.57 (to 2dp) degrees

cone volume

inscribed rhombus

a rhombus is drawn inside a regular hexagon, as shown

what must the angles of the rhombus be?

surrounding a point

semi regular tessellations

look at the regular polygons surrounding any point

what is the angle sum?

are all points surrounded in the same way for each tessellation?

Wikipedia tessellations

bits and bobs

puzzles that can involve simultaneous equations

powerpoint is here

Polya's problem

George Polya
author of 'How to Solve It'


















an adapted version of a problem credited to Polya:

fractions to recurring decimals

an opportunity to do some ('bus stop') division

having looked at thirds, ninths and elevenths

a ppt is here

see also the posting on Puntmat relating to this topic

how can you tell what number the sevenths start with?

picture from Puntmat
(originally from Wikimedia)

note that opposite digits on the circle sum to 9

again, opposite digits sum to 9

the 'length' of the 31ths blocks are only 15 digits

youtube video:
998,001
numberphile
introduced by
Dr James Grime


where did the 8 go?







31ths repeat after 15 digits
41ths repeat after only 5 digits
more information on wikipedia