Write-up 6 asked us to examine each of ten explorations
and select one of them for a write-up. I have chosen problem 4 to write-up.
Problem 4 asked me to explore the view to a picture that is 4ft by 4 ft
in size and hanfging on the wall with its bottom edge 2 ft above my eye
level. The problem asks how far back I should stand directly in front in
order to view the picture at the maximum angle. There will be two views
to consider, firstly the view in terms of angle of elevation looking up
to the picture, and secondly the angle from in front in terms of width of
To start with, a picture of the view looking from in front at a distance
2 ft from the picture. The angles OGN and OPN shown are actually measuring
the 'height' and 'width' of the viewing field.
This picture shows the view looking from 3ft in front of the picture. <OQN
measures the 'width of view, and <OHN measures the 'height' of view.
This picture is the view looking at the picture from 4 ft in front of it.
<ORN measures the 'width of the view, and<OCN measures the 'height'
of the view.
This picture displays the view from 5ft from points S and F. <OSN represents
the 'width of view, and <OFN represents the 'height' of view. The viewer
is looking up to the 4ft by 4 ft picture represented by the line segment
ON. The picture was constructed to be two units above the horizontal eye
position of the viewer as he/she stands viewing the picture.
The best angle in terms of angle of height is anywhere from 3 to 4 ft. The
angles of height from 3 and 4ft all both measured at 30 degrees. The viewer
must also take in the width of view which drops markedly from 90 degree
at 2 ft to 44 degrees at 5 ft.
Angles of view were measured at 2,3, 4 and 5 ft. These distances were sufficient
to see the decrease in view angles as the distance from the picture continued
to increase. The best view seems to be at 2 ft with a 90 degree width angle.
This combined with a 27 degree angle of height seems to offer a better view
than the 30 degree angle of height at 3 ft combined with a 68 degree width
of view. The width of view angle gets smaller the further back the viewer
stands from the picture. The viewer also needs to consider the angle of
elevation connected with each position. At 2 ft distance, the view is looking
up at an angle of 45 degrees. AT 3 ft, the angle lessens to about 40 degrees,
and 30degrees at 4 ft.
The view is more comfortable the at 4 ft than at 2 ft because the view is
not looking up at such a sharp angle. The better depth of field at 2 ft
may justify the extra looking up, unless the viewer wants to gaze at the
picture for long periods of time. mumThe maximum angle view is at 2 ft.