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Why does LaTex have random capitalisation and letter height?

Context:

So I'm sure this is a rather random question which probably has a really obvious answer, but since I couldn't find it on this site I've decided that I might as well ask it to quench my curiosity:

Question

I often see the LaTeX logo written like the following image:

LaTex

And I've always wondered why this is so? I've also seen it on this site as LaTeX.

So:

  • Why does this site have a capital T and X? Does "TeX" represent something?
  • Why do other sites have a raised A and lowered E? Does that represent anything?

Post - Note

Again, apologies if this is an obvious question and has already been asked. If so, please don't downvote, just give me the link to where it has been asked or tell me the answer. Also, I wasn't really sure what to tag this question - "syntax"?

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    There's nothing random about the raising of the letter "A" in the "LaTeX" logo or the lowering of the letter "E" in the "TeX" logo. The creator of TeX, Donald Knuth, came up with the logo that may be produced by running \TeX. Leslie Lamport (the creator of a set of TeX macros which he called "LaTeX", short for "Lamport's TeX") created the logo which may be produced by typing \LaTeX. The question as to why Knuth and Lamport chose to create these particular logos can only be answered with "Well, the designers were expressing their creativity".
    – Mico
    Aug 22 '20 at 4:49
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    Please go ahead and post an answer of your own. Please be sure to also provide a link to David Carlisle's answer to the query (La)TeX Logo - Where does it come from?
    – Mico
    Aug 22 '20 at 5:03
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    Does these answer your question ? What is the meaning of moved letters on LaTeX logo? and (La)TeX Logo - Where does it come from? There is also the fact that the TEX logo (with no letter offset) belonged to IBM.
    – AndréC
    Aug 22 '20 at 5:08
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    @Gill Closing a question is not the same as deleting the question, nor does it take away “rewards” from anyone who has answered it. (In any case, Mico has not “answered” this question in the Stack Exchange sense; he has only left a comment: only you have (self-)answered it.) A closed question remains forever (unless deleted), and remains searchable; all that closing a question does is prevent more people from adding answers to that question, and (when the question is closed as a duplicate) it serves as a notice that an earlier question exist elsewhere, possibly with more or better answers. Aug 22 '20 at 5:33
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    @AndréC -- Actually, "TEX" was owned by Honeywell. This is documented in chapter 1 of the TeXbook. It was a gentlemen's agreement that TeX for the composition software should forever be identified with a lowered "e", which in ordinary text (where the logo can't be realized) is "TeX". Aug 22 '20 at 13:51
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So, because I think @Mico is very busy answering other questions, I'll quote his comments as a separate answer to this posting):

There's nothing random about the raising of the letter "A" in the "LaTeX" logo or the lowering of the letter "E" in the "TeX" logo.

The creator of TeX, Donald Knuth, came up with the logo that may be produced by running \TeX. Leslie Lamport (the creator of a set of TeX macros which he called "LaTeX", possibly short for "Lamport's TeX") created the logo which may be produced by typing \LaTeX.

The question as to why Knuth and Lamport chose to create these particular logos can only be answered with "Well, the designers were expressing their creativity".

Well, consider my curiosity quenched... Thanks to Mico once more!

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