Here it is.

keywords: disease, injury, hazards

# Day: July 30, 2019

# derivation of the formula for the area of an ellipse

Here it is.

Also, here is a discussion of the relationship between ellipses and cones.

keywords: Mathematics, Geometry, conic sections, Calculus, integrals, integration

# lorem ipsum

Anyone who hasn’t learned Esperanto has no business saying they have ‘nothing better to do’ than hang out in cyberspace.

keywords: life, language, wisdom

# abstraction and concreteness

You can’t navigate the world without a certain level of abstraction. This goes a long way towards explaining the existence and persistence of superstition, because the fantasy constituting superstition is simply the ignoramus’s version of abstraction.

“The root of all superstition is that men observe when a thing hits, but not when it misses.”

— Francis Bacon

The counterpoint to abstraction is, of course, concreteness, and the default form of concreteness is setting to fire.

So, superstition is the default form of abstraction, and setting to fire is the default form of concreteness.

Superstition is fossilized fantasy.

Setting to fire is boundless celebration. (cf: fireworks displays; This is also why war will continue to exist as long as men consider it to be wicked. It will cease only when men consider it to be vulgar. And since boundless celebration and setting to fire are highly (positively) correlated, it follows that a place of pleasure is a dangerous place.)

The mission of the political left wing is to oppose superstition. The mission of the political right wing is to oppose setting to fire. So, the two political wings have different missions, and neither hesitates stepping in the other’s cornflakes (encroaching on the other’s domain) to achieve its ends. Hence, the two political wings are perpetually at each other’s throat.

keywords: life, General Systems Theory, navigation, prosperity, danger, correlation

# derivation of the formula for the lateral area of a right circular cone

Here it is.

Also, here is a discussion of the relationship between cones and ellipses.

And here is the Wikipedia article on pyramids.

keywords: Mathematics, Geometry

# meta data, consisting of a set of parameters

Geometric objects require meta parameters. For polygons, one such parameter is the Boolean (‘yes’ / ‘no’) variable as to whether any side length information is given. An answer of ‘no’ is colloquially referenced by saying that the triangle is ‘scalene’. (In the absence of conscious use of meta parameters, a ‘scalene’ triangle is crudely taken to be a triangle having 3 sides of unequal length.) Another meta parameter, for trapezoids, is which parallel sides (in case there are more than one pair of such) are to be considered the bases of the trapezoid, the other two sides being considered the ‘legs’ of the trapezoid, referred to colloquially as ‘the non-parallel sides of the trapezoid’ even if they are in fact parallel (in the case of a parallelogram). (Thus, the use of meta parameters eliminates the confusion as to whether a parallelogram should be considered a trapezoid. Without meta parameters, the phraseology forces a negative answer, but at the cost of making the Trapezoidal Rule (in Calculus) awkward to apply.)

Another meta parameter is the Boolean variable as to whether the geometric object is to be considered as a point-set, or as distinguished object. For example, a square, considered as a point set is not convex, but considered as a distinguished object, is (convexity for a distinguished Jordan curve being defined in terms of the convexity of the region that it bounds). Also, a square, considered as a point set, has area 0, but considered as a distinguished object, has positive area (area for a distinguished Jordan curve being defined in terms of the area of the region that it bounds). In short, lack of an acceptance of a framework of meta data causes exclusivity-based definitions. This is why such definitions are the rule in elementary school – because the concept of meta data is somewhat sophisticated and automatically presumed to be beyond the capabilities of young students – if the concept of meta data is even consciously entertained by their teachers at all. (Chesterton would likely weigh in here with something about gentle contempt.)

keywords: language, Geometry, Mathematics

# lorem ipsum

Successful navigation requires maintaining more than one perspective.

keywords: prosperity

# confusion about ‘median’

For a triangle, ‘median’ and ‘midsegment’ are two different things, the former defined in Wikipedia’s article ‘Median (geometry)’, and the latter defined in Wikipedia’s article ‘Medial triangle’. (Note that Wikipedia’s article ‘Median (geometry)’ is distinct from Wikipedia’s article ‘Geometric median’.) The confusion that we want to highlight here is that for a trapezoid, the triangle meaning of ‘median’ is not of interest and not used, but the idea of ‘midsegment’ is of interest and used, but is usually labeled with the term ‘median’ (and only occasionally labeled with the term ‘midsegment’). Such usage occurs in the nuts-and-bolts realm of mathematics homework problems and mathematics tournament problems, and so the students need to be on their toes as to this ambiguity that is not at all addressed on Wikipedia’s disambiguation page for ‘median’. It is true that in Wikipedia’s article on trapezoids the term ‘midsegment’ is used, with a parenthetical note of ‘median’ being an alternative term, but this is opposite of popular usage (the popular usage being the one given by Merriam-Webster in its free online dictionary).

keywords: language

# work in the verbal plane: canons of terminology

Here is the link to a discussion of this.

keywords: language

# formula for the area of the inner triangle formed by three Cevians

Here is the link to a presentation of it.

keywords: Routh’s formula, Mathematics, Geometry, 3 things taken 2 at a time