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Problem of the Week

Problem B

Flangles

Twenty seven flag positions, one for each of the letters from A to Z and one for a space, as given in the table.

Semaphore signal flags are used to communicate in places such as on aircraft carriers. Each letter is represented by a specific position of the two flags. Each flag is placed vertically, horizontally, or exactly halfway between the vertical and the horizontal.

Letter or Character Position of Flag in Right Hand Position of Flag in Left Hand
A down and right down
B right down
C up and right down
D up down
E down up and left
F down left
G down down and left
H right down and right
I down and right up and right
J up left
K down and right up
L down and right up and left
M down and right left
N down and right down and left
O right up and right
P right up
Q right up and left
R right left
S right left and down
T up and right up
U up and right up and left
V up down and left
W up and left left
X up and left down and left
Y up and right left
Z down and left left
Space down down

  1. Add each letter to the table below by looking at the type of angle between the two flags in the signal for that letter. Letters A and L are already placed. The ‘space’ is not a letter. It is used to put a space between words. Assume the angles are between 0\(^{\circ}\) and 180\(^{\circ}\), but can also include 0\(^{\circ}\) and 180\(^{\circ}\).

    Angle Type Letters
    Acute A,
    Right
    Obtuse
    Straight L,

    Here is how we know that the angle for letter A is acute and for letter L is straight:

    Letter A

    Position of the two flags for the letter A.Angle being measured between the two flags.

    Letter L

    Position of the two flags for the letter L. Angle being measured between the two flags.

  2. When communicating with semaphore signal flags, there are only four different angle measurements between the two flags. What are these angles? Assume the angles are between 0\(^{\circ}\) and 180\(^{\circ}\), but can also include 0\(^{\circ}\) and 180\(^{\circ}\).

  3. Try to communicate a simple message to a friend using your arms as semaphores.


Strand: Geometry and Spatial Sense