Geometrical interpretation of Taylor series for sine and cosine?

AI Thread Summary
A geometrical interpretation of Taylor series for sine and cosine has been proposed, focusing on deriving approximations through geometric constructs rather than traditional calculus methods. The author is uncertain if similar interpretations exist and is cautious about duplicating existing work. They acknowledge the increasing complexity of achieving higher accuracy in their approach. Preliminary results appear promising, prompting the intention to prepare papers for further discussion. The conversation encourages sharing detailed derivations and suggests exploring resources for visual proofs related to the topic.
waht
Messages
1,499
Reaction score
4
I've stumbled upon what might be a geometrical interpretation of Taylor's series for sine and cosine. Instead of deriving the Taylor's series by summing infinite derivatives over factorials, I can derive the same approximation from purely geometrical constructs.

I'm wondering if something like this has been done before? If so I don't want to go further and reinvent the wheel. Currently I'm stuck at a certain point because the more accurate you want to get, the complexity of this rises exponentially. But preliminary results are conclusive, this could be true. If you are aware of something like this, let me know. In the mean time I'm going to prepare some papers to show you guys if interested.
 
Mathematics news on Phys.org
Just off the top of my head I'm not aware of anything like that, but I'm just a silly undergrad. Could you describe your derivation in more detail?
 
You might want to check the "http://www.maa.org/pubs/monthly.html" ] (1970-presesnt) for "visual proofs" or "proof without words" along these lines.
 
Last edited by a moderator:

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Can Taylor series be used to get the roots of a polynomial?
Replies
16
Views
5K
Why Taylor Series works so well for some functions and not for others
Replies
3
Views
3K
Derivatives of Sine and Cosine Relationship
Replies
7
Views
3K
How to find sines/cosines without memorization?
Replies
7
Views
2K
A Taylor series expansion of functional
Replies
4
Views
3K
Not sure I get the Taylor Series
Replies
2
Views
2K
Limit of Cosine Function without Taylor Series
Replies
14
Views
2K
How to get (Taylor) series formula for arcosh?
Replies
1
Views
4K
Unitary translation operator and taylor expansion
Replies
10
Views
4K
What is the connection between sine and cosine and geometry?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top