Why is the parallelogram rule for the addition of forces as it is?

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Discussion Overview

The discussion centers around the origins and fundamental nature of the parallelogram rule for the addition of forces. Participants explore historical context, logical foundations, and the intuition behind the rule, as well as its implications in the study of forces and vector addition.

Discussion Character

  • Exploratory
  • Historical
  • Conceptual clarification

Main Points Raised

  • One participant questions the deep origins of the parallelogram rule and whether it must obey certain logical principles.
  • Another participant suggests that vector addition itself could be considered the underlying logic of the rule.
  • A historical perspective is provided, noting that the rule likely arose during a time when mathematics was primarily geometric, referencing the work of Stevens.
  • It is mentioned that the parallelogram rule enforces the addition of vector components.
  • One participant highlights that the rule is based on the principle of linear superposition of forces, indicating that forces do not interfere with one another, thus forming a linear vector space.
  • The rule's historical roots are traced back to at least the first century BC, with references to Heron's "Mechanics" and the observation of ropes as a source of intuition.
  • Participants express gratitude for the detailed information shared, indicating a collaborative exploration of the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the fundamental nature of the parallelogram rule or its origins, with multiple viewpoints and historical interpretations presented throughout the discussion.

Contextual Notes

Some claims rely on historical interpretations that may not be universally accepted, and the discussion includes references to specific historical figures and texts that may require further exploration for clarity.

zexott
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Why is the parallelogram rule for the addition of forces as it is?
I feel it must have some deep origin and pointing to something fundamental. Though I know this problem may have no answer: God design it as such.
But I wonder how the first person came up with this rule, where does his/her intuition come from?
Are there something that addition of forces simply must obey due to logic itself?
Are there active research going on that is investigating this?
 
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Would you accept vector addition as being the logic?
 
It is likely that it arose because, at the time this was being developed, probably at the time of people like Stevens (1548 - 1620) most mathematics was carried out geometrically. So the parallelogram construction was the natural mode of working.
 
Whoops, autocorrect jumped in. I mean Stevenus .
 
Use the Edit button to correct it.
 
All the parallelogram rule does is to enforce that the addition of two vectors actually add their components.
 
Historically it was an observation about ropes. The rule is equivalent assuming the rule of linear superposition of forces ... that is, application of one force does not interfere with any other. This means that forces form a linear vector space.

The rule dates back to at least the first century BC; it appears in Heron's "Mechanics". But it is probably older.

Philosophers have written on it: file:///C:/Users/Peter/Downloads/1548-24248-1-PB.pdf
 
UltrafastPED said:
Historically it was an observation about ropes. The rule is equivalent assuming the rule of linear superposition of forces ... that is, application of one force does not interfere with any other. This means that forces form a linear vector space.

The rule dates back to at least the first century BC; it appears in Heron's "Mechanics". But it is probably older.

Philosophers have written on it: file:///C:/Users/Peter/Downloads/1548-24248-1-PB.pdf

Ah, observation of ropes, that's how their intuition comes. Now it seems conceivable for me. Your information is very detailed and now I guess I can trace it down. Thank you so much! And thank you all for your time and attention!
 
UltrafastPED said:
file:///C:/Users/Peter/Downloads/1548-24248-1-PB.pdf

:smile:
Don't you have a web link?
 
Last edited:

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