Category: Stranger than fiction (nonfiction)

V838 Monocerotis a spectroscopic binary star system (a binary star evident from the Doppler effect) in the constellation Monoceros about 19,000 light years from the Sun. Identified as a luminous red novae, thought to have been [caused by the] merger of two stars within a triple system.

A light echo is a physical phenomenon caused by light reflected off surfaces distant from the source, and arriving at the observer with a delay relative to this distance. The phenomenon is analogous to an echo of sound

In the case of V838 Monocerotis, the light echo produced was unprecedented and is well documented in images taken by the Hubble Space Telescope. While the photos appear to depict an expanding spherical shell of debris, they are actually formed by the illumination of an ever-expanding ellipsoid with the progenitor star at one focus and the observer at the other. Hence, despite appearances, the structures in these photos are actually concave toward the viewer.

Source Wikipedia: V838 Monocerotis, Light echo

From: Chapter 10, Mathematics for the Nonmathematician, Morris Kline

Let us accept, then, the principle that the canvas must contain the same section that a glass screen placed between the eye of the painter and the actual scene would contain. Since the artist cannot look through his canvas at the actual scene and may even be painting an imaginary scene, he must have theorems which tell him how to place his objects on the canvas so that the painting will, in effect, contain the section made by a glass screen.

Suppose then that the eye at E (Fig. 10–8) looks at the horizontal line GH and that GH is parallel to a vertical glass screen. The lines from E to the points of GH lie in one plane, namely the plane determined by the point E and the line GH, for a point and a line determine a plane. This plane will cut the screen in a line, G′H′, because two planes which meet at all meet in a line. It is apparent that the line G′H′ must also be horizontal, but we can prove this fact and so be certain. We can imagine a vertical plane through GH. Since GH is parallel to the screen and the latter is also vertical, the two planes must be parallel. The plane determined by E and GH cuts these parallel planes, and a plane which intersects two parallel planes intersects them in parallel lines. Hence G′H′ is parallel to GH, and since GH is horizontal, so is G′H′. But GH was any horizontal line parallel to the screen. Hence the image on the screen of any horizontal line parallel to the screen or picture plane must be horizontal. Thus in a painting which is to contain what this glass screen contains, the line G′H′ must be drawn horizontally.

We can present practically the same argument to show that the image of any vertical line, which is automatically parallel to the vertical screen, must appear on the screen as a vertical line. Thus all vertical lines must be drawn vertically. Continue reading “SOME MATHEMATICAL THEOREMS ON PERSPECTIVE DRAWING”

Vowels diacritics

Consonants

Conjunct consonants

Punctuation

Numerals

French Dieu
Spanish Dios from
Latin Deus from 
Ancient Greek Zeus from
Proto-Hellenic *dzéus from
Proto-Indo-European *deiwos meaning "celestial" or "shining"

Iuppiter or Jūpiter from
Roman Diespiter (deus + Latin: pater = English: father) from 
Proto-Italic *djous patēr from
Proto-Indo-European root *Dyḗws*Pahtḗr 
	literally meaning "Sky Father"
Whence is also derived the name of the Hindu sky god Dyáuṣ Pitṛ́ (Vedic Sanskrit: Dyáuṣpitṛ́)
and Proto-Germanic *Tīwaz or Tius hence Old Norse Týr 

English mother from 
Middle English moder from 
Old English mōdor from 
Proto-Germanic *mōdēr from 
Proto-Indo-European *méh₂tēr 
Other cognates include 
  Spanish madre
  Latin māter
  Greek mā́tēr/mā́tar 
  Slavic *mati 
  Persian madar
  Sanskrit mātṛ 

English Sin from
Old English synn "moral wrongdoing" from 
Proto-Germanic *sundiō probably "it is true" from 
Proto-Indo-European *snt-ya-, a collective form from 
*es-ont- "becoming" 
  present participle of root *es- "to be"

Sanskrit Bodhisattva "one whose essence is perfect knowledge," from 
bodhi "perfect knowledge" + sattva "reality, being" from 
sat-, sant- "existing, true, virtuous" from 
Proto-Indo-European root *es- "to be"

Click on images for greater detail.

Constellations (modern) key, by family and year established, and ecliptic:

Constellations map (see key above):

Constellations of Northern Hemisphere:

Constellations of Southern Hemisphere: