Liberal Arts Blog — Triangulation — Three Meanings
Liberal Arts Blog — Monday is the Joy of Math, Statistics, and Numbers Day
Today’s Topic — Triangulation — Three Meanings (locating, strengthening, manipulating)
Triangles are magic. They serve all kinds of purposes. Take three. Locating an object, say a ship. Strengthening a structure with diagonals to form a network of trusses. Manipulating someone to get your way by bringing in a third party. Experts — please chime in. Correct, elaborate, elucidate.
SET BASELINE, MEASURE TWO ANGLES, MAKE A MINI VERSION, ANALOGIZE
1. Make baseline — from Point A to Point B each equidistant from midpoint. Measure it.
2. Measure the angles from each point to the object from points A and B.
3. Replicate the triangle in miniature and extend the lines until they intersect. Measure distance from the baseline to the object.
NB: Then calculate the ratio of the miniature baseline to the actual baseline. Multiple that ratio times the length from the baseline to the top vertex of the mini-baseline. Voila!
MAKING A TRUSS — THE BASIC UNIT OF THE EIFFEL TOWER
1. Egyptians used rope triangles (“trusses”) to stabilize masts.
2. Gustave Eiffel used triangles to build the world’s tallest structure in 1889.
3. Squares tend to collapse without diagonal support. Examples all around you: the standard bicycle frame consists of two triangles. The triangular top of houses consists of rafters sloping down connected at the base by joists.
THE PSYCHOLOGY OF TRIANGLES — VARIATIONS ON A THEME
1. Children learn it very early — how to pit one parent against the other to get their way. A healthy developmental milestone? 18 months?
2. “In the context of narcissism, triangulation occurs when the narcissist attempts to control the flow, interpretation, and nuances of communication between two separate actors or groups of actors. Ensuring communications flow through, and constantly relate back to the narcissist provides a feeling o of importance.”
3. The Karpman Drama Triangle: the Victim (“poor me”), the Rescuer (“Let me help you”), and the Persecutor (“It’s all your fault.”) Maps a toxic process of co-dependency. Above a positive vision of transformation.
So what are your personal favorite magic numbers? What do they stand for? Please share the coolest thing you learned this week related to math, statistics, or numbers in general. Or, even better, the coolest or most important thing you learned in your life related to math.
This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.