Talk:Simpson's rules (ship stability)

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third rule needs details

The third rule is listed as $Area={\frac {h}{12}}(5a+8b-c)$ , without any indication what $a$ , $b$ and $c$ are. For the other two rules the images give hints, here there is no image. I didn't succeed to find any reference to this version of the rule outside of this page, and it looks quite strange. (I don't own the book which is used as a reference here.) Can anyone help here, or should we remove that one? -- Paul Ebermann (talk) 19:29, 3 July 2017 (UTC)[reply]

It's described in the reference by Bhange. It gives an estimate of the area between x = x₀ and x = x₁ = x₀ + h, using not only y₀ = a and y₁ = b, but also the additional information that y₂ = c (where x₂ = x₁ + h). In the picture for Simpson's First Rule, it uses all of the data shown but estimates only the area of the left half. (Note that if you wanted to estimate the area of the right half instead, then you would reverse the roles of a and c and get (h/12)(−a + 8b + 5c). Then add the areas of the two halves together, and you get (h/12)(4a + 16b + 4c), which simplifies to Simpson's First Rule. So the two halves together add to the whole.) ―Toby Bartels (talk) 19:13, 31 January 2020 (UTC)[reply]

Merge with Simpson's rule?

This isn't really a separate topic. This simply notes that one application of Simpson's Rule is to measuring the area of water displaced by a ship. The only new thing here is the third rule, which could certainly be mentioned on the main page (where there is also the notation to explain it better). At any rate, the two pages should communicate better with each other. (I'll add in some cross-referencing.) ―Toby Bartels (talk) 19:18, 31 January 2020 (UTC)[reply]