Sončne ure pri poučevanju matematičnih in fizikalnih vsebin

Šabeder, Aljaž

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Title:	Sončne ure pri poučevanju matematičnih in fizikalnih vsebin
Authors:	ID Šabeder, Aljaž (Author) ID Mencinger, Matej (Mentor) More about this mentor... ID Repnik, Robert (Mentor) More about this mentor...
Files:	MAG_Sabeder_Aljaz_2016.pdf (5,86 MB) MD5: 6E487C025DD3457E3701BB84AE7D3101
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V magistrskem delu je obravnavana problematika sončnih ur iz matematičnega in fizikalnega vidika. Podan je pregled različnih tipov sončnih ur s poudarkom na ekvatorialnih sončnih urah. Podrobno je razloženo delovanje ekvatorialnih ur in analematične sončne ure, ki so lahko vključene v posamezne vsebine pri poučevanju v osnovnih in srednjih šolah. Razlaga delovanja sončnih ur temelji na Keplerjevih zakonih, navideznem potovanju Sonca čez nebesno sfero, geometriji in enačbi stožnic (predvsem elipse). Poglobljeno je razložena osnova nebesne mehanike s poudarkom na sfernih koordinatnih sistemih (horizontskem in ekvatorialnem), ki so ključni za določanje koordinat nebesnih teles na nebesni sferi. Obravnavana je razlika med dnevnim in letnim gibanjem Sonca in posledično med dnevnim in letnim gibanjem sence, ki jo opiše konec (navpične) palice (gnomon). Opisana je razlika med zvezdnim (siderskim), sončnim (sinodskim) in povprečnim dnevom, ki so ključni pri umerjanju sončne ure. S tem namenom so pojasnjene tudi vse korekcije časa, s katerimi lahko ločimo med časom, ki ga kaže sončna in ročna ura. Ena izmed glavnih korekcij je zagotovo enačba časa, ki nam pove za razliko med pravim in srednjim Soncem. Opisan je način za iskanje lokalnega meridiana, ki je poleg določanja geografske širine in dolžine kraja, na kateri je sončna ura, ključen za njeno konstrukcijo. Podrobneje je predstavljena odvisnost urnih črt posameznih sončnih ur, ki so narisane na njihovih številčnicah. Za lažjo predstavo so omenjene številčnice predstavljene tudi na grafični način z matematičnim programom Geogebra. Raziskani so učni načrti predmetov matematike, fizike in astronomije v srednjih in osnovnih šolah ter učne vsebine, pri katerih je tematika sončnih ur lahko vpeljana v redno izobraževalno snov.
Keywords:	sončne ure, Keplerjevi zakoni, nebesna mehanika, dnevno in letno navidezno gibanje Sonca, zvezdni dan, sončni dan, enačba časa, lokalni meridian, urne črte, stožnice, sferni koordinatni sistem.
Place of publishing:	Maribor
Publisher:	[A. Šabeder]
Year of publishing:	2016
PID:	20.500.12556/DKUM-62461
UDC:	37.091.3:51/53(043.2)
COBISS.SI-ID:	22560776
NUK URN:	URN:SI:UM:DK:XTIPVRIG
Publication date in DKUM:	21.09.2016
Views:	2529
Downloads:	363
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	Sundials at teaching mathematics and physics in primary and secondary schools
Abstract:	The problem of sundials is discussed from the mathematical and physical point of view. A review of several types of equatorial sundials is presented. The origin of equatorial, analematic and polar sundials is explained. In particular, some original ideas how to include the topics of sundials in some related contents in teaching at elementary and secondary schools is considered. The interpretation of functioning of the sundials is based on Kepler's laws, the virtual movement of the Sun over the celestial sphere, the geometry and conics section equations (in particular of ellipses). More in-depth explanation of how the sundials work is given by the basis of celestial mechanics with the emphasis on spherical coordinate systems (horizontal and equatorial). Horizontal and equatorial coordinate systems are known to be crucial for determining the coordinates of celestial bodies on the celestial sphere. The difference between the daily and annual movement of the sun and consequently the difference between the daily and annual movements of the shadow (of the gnomon) is described. The difference between astronomical, solar and the average day is considered. All this different times and the corresponding time corrections are crucial for the calibration of the sundial. Finally, the difference between the time which is shown by the sundial and the time obtained from our clock (i.e. the local time) is explained. One of the main corrections is certainly the equation of time, which tells us the difference of time between the true and the mean Sun. A method for finding the local meridian is also described. In addition to the determination of latitude and longitude of the location of the sundial, the local meridian is crucial for its construction. More details are presented within the dependency of hour lines of several sundials. The hour lines are drawn on the face of the sundials, which is for the sake of simplicity, presented in the graphical mode using the mathematical program Geogebra. The curricula of mathematics, physics and astronomy in primary and secondary schools is researched and some learning contents in which the sundials topic can be introduced or involved into the regular educational subject matter is presented.
Keywords:	Sundials, Kepler's laws, celestial mechanics, daily and annual movement of the Sun, astronomical day, solar day, equation of time, local meridian, hour lines, conics, spherical coordinate, sferical geometry.

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