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The curve, also in mathematics called a curved line in theoretical and applied mathematics texts is the mathematical object similar or different to the axial straight plane lines, the curved line is not a straight line but may be a function, or the curved line may be part of a non straight plane (nonrectangular object), or part of a sphere or spherical object, or a curved plane, etc., and there too is different to straight lines that are part of straight planes but for some functions may be projected to a straight plane into straight planes.
A plane algebraic curve is the zero set of a polynomial in two indeterminates. More generally, an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic variety of dimension one. If the coefficients of the polynomials belong to a field k, the curve is said to be defined over k. In the common case of a real algebraic curve, where k is the field of real numbers, an algebraic curve is a finite union of topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a surface, and is often called a Riemann surface. Although not being curves in the common sense, algebraic curves defined over other fields have been widely studied. In particular, algebraic curves over a finite field are widely used in modern cryptography.
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Julia Fractal Mandala
Thanks for your visits, faves and comments! They are much appreciated! Stay safe & have a great day!
Julia Fractal
Thanks for your visits, faves and comments! They are much appreciated! Stay safe & have a great day!
Pi Day is an annual celebration of the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in the month/day format) since 3, 1, and 4 are the first three significant digits of π.
It was founded in 1988 by Larry Shaw, an employee of the Exploratorium. Celebrations often involve eating pie or holding pi recitation competitions. In 2009, the United States House of Representatives supported the designation of Pi Day. UNESCO's 40th General Conference designated Pi Day as the International Day of Mathematics in November 2019.
The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics and the earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, and is spelled out as "pi". It is also referred to as Archimedes' constant
Being an irrational number, π cannot be expressed as a common fraction, although fractions such as 22/7 are commonly used to approximate it. Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern. Its decimal (or other base) digits appear to be randomly distributed, and are conjectured to satisfy a specific kind of statistical randomness.
It is known that π is a transcendental number: it is not the root of any polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematics approximated π to seven digits, while Indian mathematics made a five-digit approximation, both using geometrical techniques. The first exact formula for π, based on infinite series, was discovered a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics.
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Il 14 marzo (o 3,14) è il giorno del Pi greco: una festa per chi ama la matematica
Il simbolo che conosciamo fu usato per la prima volta circa 250 anni fa, dal matematico gallese William Jones nel trattato A New Introduction to Mathematics (1706). π è l'iniziale dei termini greci περιφέρεια, "periferia", e περίμετρος, "perimetro", con riferimento alla circonferenza; ma anche del filosofo e matematico Pitagora. Prima di allora per riferirsi alla costante si ricorreva a complesse perifrasi come: "la quantità che quando si moltiplica per il diametro, dà la circonferenza".
IL CALCOLO DEI SUOI DECIMALI HA FATTO IMPAZZIRE INTERE GENERAZIONI. π è irrazionale, cioè non esprimibile come una frazione di due numeri interi: le 100 cifre riportate qui sopra sono insomma uno sforzo contenuto, rispetto a un numero che procede in apparenza all'infinito. Il record attuale di decimali verificati è di 22.459.157.718.361, frutto del lavoro di un centinaio di giorni di un supercomputer svizzero.
Defocus is modeled in Zernike polynomial format as a(2 \rho^2-1), where a is the defocus coefficient in wavelengths of light. This corresponds to the parabola-shaped optical path difference between two spherical wavefronts that are tangent at their vertices and have different radii of curvature.
The dying Tierberg glaciar - view from the Tierbergsattel (2700m). Highly recommended for mountaineers and hikers.
It was a beautiful sunny day with stable weather conditions.
Any criticism is welcome, wether negative or positive!
Have a nice day!
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SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 2099 / length of data axis 1
NAXIS2 = 3757 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
PROGRAM = 'Siril 1.4.0-beta4' / Software that created this HDU
DATE = '2025-10-28T19:05:26' / UTC date that FITS file was created
ROWORDER= 'TOP-DOWN' / Order of the rows in image array
FILTER = 'mixed ' / Active filter name
FOCALLEN= 252.209 / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 2.9 / [um] Pixel X axis size
YPIXSZ = 2.9 / [um] Pixel Y axis size
STACKCNT= 1 / Stack frames
OBJCTRA = '00 42 51.085' / [H M S] Image center Right Ascension
OBJCTDEC= '+41 16 0.533' / [D M S] Image center Declination
RA = 10.7128533944096 / [deg] Image center Right Ascension
DEC = 41.2668147570075 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 2000. / Equatorial equinox
CRPIX1 = 1050. / Axis1 reference pixel
CRPIX2 = 1879. / Axis2 reference pixel
CRVAL1 = 10.7128533944096 / [deg] Axis1 reference value
CRVAL2 = 41.2668147570075 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000658961310833057 / [deg] X pixel size
CDELT2 = 0.000658657482781499 / [deg] Y pixel size
PC1_1 = 0.965466545738584 / Linear transformation matrix (1, 1)
PC1_2 = -0.260527060129284 / Linear transformation matrix (1, 2)
PC2_1 = 0.260649538636549 / Linear transformation matrix (2, 1)
PC2_2 = 0.965433487097145 / Linear transformation matrix (2, 2)
A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = -2.80336019035679E-08
A_1_1 = -3.80046040636165E-08
A_0_2 = 2.15136589084034E-08
A_3_0 = -8.44778011308703E-12
A_2_1 = 3.79062635145127E-11
A_1_2 = -6.73187841369515E-12
A_0_3 = -5.31267099415704E-12
B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = 6.50165301873809E-08
B_1_1 = -6.82755638990518E-08
B_0_2 = -3.78736345908275E-08
B_3_0 = -7.45737245754271E-11
B_2_1 = 7.05330412318602E-11
B_1_2 = 8.38780163680683E-11
B_0_3 = 5.13524191910021E-11
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = -3.57525790723625E-06
AP_1_0 = 2.47316700452416E-09
AP_0_1 = 3.73883575289199E-09
AP_2_0 = 2.80403591982289E-08
AP_1_1 = 3.80143220778317E-08
AP_0_2 = -2.15052126818701E-08
AP_3_0 = 8.44192075868852E-12
AP_2_1 = -3.79051854941149E-11
AP_1_2 = 6.72593013181604E-12
AP_0_3 = 5.30678663674559E-12
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = 2.85441348217358E-05
BP_1_0 = -3.77519182233627E-08
BP_0_1 = -4.91273611791243E-08
BP_2_0 = -6.50606832475918E-08
BP_1_1 = 6.82141794273729E-08
BP_0_2 = 3.78348315070649E-08
BP_3_0 = 7.45971929861121E-11
BP_2_1 = -7.04663131493368E-11
BP_1_2 = -8.37886776768878E-11
BP_0_3 = -5.13086278498007E-11
HISTORY Saturation enhancement (amount=0.45)
HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)
HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)
HISTORY Saturation enhancement (amount=0.49)
END
This is the blue version of Pink Chaos...
The equation was a complex polynomial mapped to the complex plane. The original colour was pink, I have changed the hue and saturation in PSE.
Found that one lucky fractal that happened to look a bit like the Alien..
The Polynomial
@3000x3000, in-game downsampling
Gamma, exposure, saturation edited in-game
Dramatouch (alt version)
The Polynomial
@5600x2625, in-game downsampling
Gamma, exposure, saturation edited in-game