circular perimeter

this problem is from David Wells' collection in 'curious and interesting geometry'
does the line always bisect the perimeter?

the powerpoint goes through a special case and the general case

arc length and sector area

a powerpoint is here

trying to obtain answers without too many decimal places - maybe misguidedly!

radius from arc details

one way to work out the radius of an arc (r) from a given height (h) and the length of the chord (L)

is to use the formula

which can obtained from the intersecting chord theorem or by using pythagoras

check that this gives the correct radius for the 'grate' question

grate question

fire grates come in sizes that are the arc length of the front edge

a manufacturer provides these dimensions for a '16 inch' grate:

assume that the centre of the arc is at the back edge of the grate:

calculate the length of the front arc in mm

convert to inches using 25.4 mm = 1 inch

is the arc length close to 16" ?


the dimensions for other grate sizes are:
12" = 280mm, 220mm, 170mm
14" = 330mm, 240mm, 210mm
what are the arc lengths of these grates?

skyhawk

the 'Skyhawk' ride opened at Cedar Point, in Cleveland Ohio in 2006












the arms are 84 feet in length
the maximum swing goes 120 degrees either side of the vertical (yes, 120 degrees - yikes)

what is the arc length for this maximum swing?

video clips show the swing in operation - either on Vimeo or YouTube

swinging

lengths of arcs
by swinging