Talk:Area of Triangle Inscribed in Parabola

So ProofWiki doesn't want the Notes section just deleted. Is it (1) just clutter, (2) would be OK as a Corollary. (3) would be OK as a separate page?. --Telliott99 (talk) 20:22, 31 October 2023 (UTC)

Apologies, deleted too much, but indeed, it's either germane to the proof, in which case it belongs in the proof, or it's not, in which case it goes on a page raising it as a valid result in its own right. --prime mover (talk) 01:11, 1 November 2023 (UTC)

I'm not getting it. We can simply define $C_x$ as $\dfrac 1 2 \paren {u + v}$. Then later, when we already have the base and the altitude, why do we need the sine of the angle? It just seems like excess baggage to me. --Telliott99 (talk) 19:40, 3 November 2023 (UTC)

We don't have the Altitude of the Triangle. By definition -

Let a perpendicular be dropped from $\angle A$ to its opposite side $a$:

The line $h_a$ so constructed is called the altitude of $\angle A$.

Where is the perpendicular in this picture?

--Robkahn131 (talk) 20:14, 3 November 2023 (UTC)

Beg to differ. Looking through ProofWiki, it does not seem to be defined here, but it is well understood that the altitude of an obtuse triangle lies outside the triangle. Here it is simply (u-v)/2. --Telliott99 (talk) 20:40, 3 November 2023 (UTC)

Perhaps you could amend our definitions to clarify this point? The whole point of definitions is to ensure we do not need to rely on anything being "well understood". It is written down for dummies like me. :-) --Robkahn131 (talk) 20:55, 3 November 2023 (UTC)

My understanding is that I do not have the status to write Definitions. --Telliott99 (talk) 22:02, 3 November 2023 (UTC)

Wot? Seriously? Have you tried? --prime mover (talk) 23:55, 3 November 2023 (UTC)

Read it here somewhere. Something about definitions with no attribution that turned out badly. However now I find Help:FAQ/Questions about House Conventions/Definition or Statement of Equivalence so I will study up. --01:21, 4 November 2023 (UTC)

What you clearly misunderstood was my dissatisfaction at contributors who in the past have posted up inaccurate material which is not subsequently caught for some time. There's nothing in your username's authorisations that prevents you posting up definitions. What we do is request that you provide a source for every definition you post, or if not, add the template that notifies the team that there is no source quoted.

I would suggest that you browse the site and study already-written examples of how pages are to be presented. It is possible to pick up the style quickly. Others have done so. --prime mover (talk) 01:50, 4 November 2023 (UTC)

Just to be clear, I don't think the last revision adds anything useful and it has provoked a call for refactoring. So I am done with the page, unless you all have a better idea. I would be happy to write something with the notes that I had before as a separate page. --Telliott99 (talk) 22:04, 3 November 2023 (UTC)

Just to be clear, notes for work to be done assigned to maintenance templates are not intended necessarily for the writer of the page to sort out. We have a standard look and feel which, when adhered to rigorously, makes comprehension of a page straightforward and easy. The style is terse and (as far as possible) minimalist. As you may appreciate, writing mathematical proofs in such a style is challenging, and it takes time to develop the skills so to do. Hence we (collectively, as a team) spend a lot of time keeping the presented work as tidy as we can. Tidy page, tidy mind, tidy understanding. --prime mover (talk) 23:54, 3 November 2023 (UTC)

I see you approve what was done. Got it. --Telliott99 (talk) 01:21, 4 November 2023 (UTC)

I say, respectfully, I do not see how the last edit adds anything that was needed. $C_x$ is defined to be $(u+v)/2$ (halfway between $u$ and $v$), and $C_y$ comes from $y = x^2$. $P_x$ is defined to be equal to $C_x$.

By drawing two similar right triangles (which could be helpful) one obtains $P_y$ as halfway between $u^2$ and $v^2$. The only thing that was missing is a proper definition of the altitude for an obtuse triangle. --Telliott99 (talk) 10:42, 4 November 2023 (UTC)

There is nothing stopping you from erasing some or all of the edits. My intention was to clarify several points made, but it may very well muddy the waters for others. Two heads are better than one - perhaps you might keep just one of the least bad edits made?  :). --Robkahn131 (talk) 15:22, 4 November 2023 (UTC)

Not allowed. See above. --Telliott99 (talk) 16:31, 4 November 2023 (UTC)

What do you mean, "not allowed"? --prime mover (talk) 16:56, 4 November 2023 (UTC)