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today's WAD, in part: tangential (tan-JEN-shuhl) adjective ... 3. Mathematics: Of or pertaining to the nature of a tangent.
Do others share my feeling that there is room for improvement in this part of the definition provided?
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Well, there is a lot to say about "tangent".
For example, it has a trigonometric meaning = sinus(x) divided by cosinus(x)... But how can I show the true meaning without a drawing?
Also, about a line tangent to a given curve, say for example a circle.. Take two points on the circle, and draw the line between themselves. This is a secant line. Then, think of the two points as approaching more and more between themselves...that line moves, and at the limit of the process it becomes the tangent line - you can say that it intersect the circle in two coincident points......And..... stop me..... this is my field...
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And of course I can talk a lot about all the words of this week.
For example
osculate - Osculating curves means literally kissing curves. I am always joking during my lessons about
hiperosculating conics...
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room for improvement in this part of the definition
Well, maybe, but is that the place for it? Tangent should be given its own definition. Look for it there.
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one of the 'rules' of lexicography is to define every word used in a definition. obviously you don't do that *within each definition. (see faldage) another rule, given the first, is be succinct.
this is a problem encountered when quoting definitions "out of context". (this is also why I don't call my "word list" a dictionary)
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... sinus(x) divided by cosinus(x)... Would the answer then be scripted as "tangentus"? My question is one mostly void of any basis in romance languages which to refer, yet the "us" suffix *seems latin in nature, and/yet is ommited 'ere in the US (eg. sine and cosine).
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emanuela: hiperosculating conics -- does speed of motion increase, somewhat like f(x)= sin (1/x) as x --> 0?  (which function would, speaking non-tangentially, constitute mathemapornography with a self-evident point of extreme singularity) ]
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Blushing..just a mistake, made from the italian seno e coseno...I should know..
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simpler than that, two hyperosculating conics have 4 coincident points in common.
No more than four, since for 5 points in a general position there is one and just one conic.
I would never have imagined to state such mathematical theorems and definitions here!
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It sure would be helpful to see a diagram of hyperosculating conics... The extraordinary mental image I have is of two connected snow cones in whirling about with crushed ice being thrown hither and thither at great speed. Such are the impressions of the uninitiated...
WhirlingWind
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