ACA 2025　Official Site

Cooperation of KeTCindyJS and Maxima(Jul 15th 10:00-10:30) 　Demonstration Site

• Compare errors using Taylor expansion as an example
Numerical differentiation in the Cindy script is based on the central difference method.
The differentiation is accurate up to the fifth order,
but significant deviations occur from the sixth derivative onward.
It may seem a bit surprising that the values suddenly deviate so significantly,
but theoretically, this is due to the limitations of floating-point representation.
For more information about floating-point numbers, please refer to the wizard zines website.

• Compare errors using Taylor expansion as an example 2
When approximating the concept of a limit,
it is not necessarily true that "the smaller the infinitesimal h, the better."
As shown in the video below, the reality is different.
Extremely small values can easily introduce errors due to theoretical limitations,
such as loss of precision or the emergence of incorrect values
when the lower-order digits are lost upon reaching the limits of numerical representation.
This kind of behavior can be observed in the video below.
Due to the limitations of floating-point numbers,
the computed values can become unstable—resulting in zero, NaN (Not a Number), or infinity. By increasing the value of h,
it is possible to maintain the accuracy of the approximation.

• Examples of teaching materials
　1. Taylor expansion
　2. Solution of an nth-degree equation
　3. Envelope
　4. Sign chart
　5. Differential equation

• KeTCindy ChatBot
We are currently developing a chatbot specialized for KeTCindyScript.

• Cooperation Test KeTCindyJS and Algebrite
I'm considering the integration of KeTCindyJS and Algebrite.

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