What's the use of subtangent and subnormal lines?

  • Context: MHB 
  • Thread starter Thread starter logan3
  • Start date Start date
  • Tags Tags
    Lines
Click For Summary
SUMMARY

The discussion centers on the relevance of subtangent and subnormal lines in modern mathematics. Participants express skepticism about their practical applications, noting that these concepts are considered archaic and largely obsolete since the early 20th century. Instead, they suggest using trigonometric functions such as sine and cosine to describe tangent lines, highlighting a more contemporary approach to understanding these relationships.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly derivatives and tangent lines.
  • Familiarity with trigonometric functions, specifically sine and cosine.
  • Knowledge of the historical context of mathematical concepts and their evolution.
  • Ability to interpret mathematical relationships and equations.
NEXT STEPS
  • Research the historical significance of subtangent and subnormal lines in calculus.
  • Explore the applications of sine and cosine in describing tangent lines in modern mathematics.
  • Investigate alternative mathematical concepts that have replaced subtangent and subnormal lines.
  • Learn about the evolution of mathematical terminology and its impact on teaching and understanding calculus.
USEFUL FOR

Mathematics students, educators, and anyone interested in the historical development of calculus concepts and their current applications in mathematical analysis.

logan3
Messages
83
Reaction score
2
What would be the point of knowing information about the subtangent and subnormal lines? Do they have any worthwhile real-world applications? Wikipedia says that they are archaic and fell into disuse after the early 20th century.

Thank-you
 
Physics news on Phys.org
logan3 said:
What would be the point of knowing information about the subtangent and subnormal lines? Do they have any worthwhile real-world applications? Wikipedia says that they are archaic and fell into disuse after the early 20th century.

Thank-you

Hi logan3! :)

First time I see them and I'm not aware of any case where we may want to use them.
Instead it makes more sense to use the cosine respectively the sine to describe the tangent line.
The relation is:
$$\cos\phi = \frac{\text{subtangent}}{\text{tangent}}\\ \sin\phi = \frac{\text{subnormal}}{\text{tangent}}$$
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 53 ·
2
Replies
53
Views
6K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
17
Views
3K
  • · Replies 17 ·
Replies
17
Views
3K