Tsukitakemochi

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July 2015

Hi there! Thank you for your contributions to Wikipedia.

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I noticed your recent edit to Triangle circumcenter vector does not have an edit summary. Please be sure to provide a summary of every edit you make, even if you write only the briefest of summaries. The summaries are very helpful to people browsing an article's history.

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Please use the edit summary to explain your reasoning for the edit, or a summary of what the edit changes. Thanks! 220 of ^Borg 03:18, 26 July 2015 (UTC)

Proposed deletion of Triangle circumcenter vector

The article Triangle circumcenter vector has been proposed for deletion because of the following concern:

Reads like a manual or textbook as indicated in {{Multiple issues}}.

While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. GeoffreyT2000 (talk) 13:53, 26 July 2015 (UTC)

Continued discussion of orthocenter

Since this is your own work, we can not use it in the article and so it would be inappropriate to continue discussing it on the talk page of that article. However, I did want to respond to some of your comments, so I moved the discussion here where it is proper to do so. You wrote:

To Bill Cherowitzo:

Thank you for your suggestion and precise correction. I really appreciate. It would be my precious resource in studying English.

As you pointed, main equation (3) itself is my own work prepared on this occasion. An equation to get circumcenter which also is on a Wikipedia's page is also by my past proposal.

In spite of your suggestion, fact that two altitudes always cross is not a mysterious one for me, because two lines always cross except they are parallel. As two sides of a triangle cannot be parallel, altitudes that are vertical to them cannot be parallel.

Three altitudes, however, do not meet at a single point except there is some good fortune. For one thing, I wanted to point it out.

Orthocenter can be either defined as "point two altitudes cross" or "point all three altitudes pass". Difference is not a matter of importance, because they are the same thing as long as "point on two altitudes is necessarily on three altitudes" is somehow testified, which, I believe, had not been done until my proposal at least on the page.

Tsukitakemochi (talk) 13:52, 14 May 2017 (UTC)

Since you raise several issues, I'd like to respond to them one at a time.

In spite of your suggestion, fact that two altitudes always cross is not a mysterious one for me, because two lines always cross except they are parallel. As two sides of a triangle cannot be parallel, altitudes that are vertical to them cannot be parallel.

My issue was not with the difficulty of the statement, but rather with the informal way you treated it by saying that it was apparent. Perhaps I did not make myself clear enough. In all the proofs of this result that I have seen, this point comes up and different authors deal with it differently, but none dismiss it as trivial. Often, because it is a simple argument, it is left to the reader, while others give a short explanation as you have given above. How you handle this depends, in part, on who you are writing the proof for. The more sophisticated you expect your audience to be, the less you have to write.

Three altitudes, however, do not meet at a single point except there is some good fortune. For one thing, I wanted to point it out.

Actually, any time that any three lines are concurrent is remarkable. Perhaps this point should be made more often.

Orthocenter can be either defined as "point two altitudes cross" or "point all three altitudes pass". Difference is not a matter of importance, because they are the same thing as long as "point on two altitudes is necessarily on three altitudes" is somehow testified, which, I believe, had not been done until my proposal at least on the page.

From a pedagogical point of view it would be much better to say that the orthocenter is defined as the intersection of the three altitudes, but it can be described (or determined) as the intersection of any two altitudes. If one does it this way, then the property ("being determined") follows immediately from the definition. If you did this the other way, then you would need to prove a theorem that stated that the three altitudes are concurrent. (You still need to prove this with the other definition, but all I am trying to say is that there is a difference that depends on what you choose as your definition.)--Bill Cherowitzo (talk) 03:19, 16 May 2017 (UTC)