Modelling of real kinematics situation as a method of the system approach to the algorithm development thinking

Transcription

1 Issue 4, Volume 4, Modelling of eal kinematics situation as a method of the sstem appoach to the algoithm development thinking Stepan Hubalovsk Abstact - One of the most impotant tasks in teaching of algoithm development and pogamming is to use a suitable method of developing theoetical knowledge of algoithm development and pogamming. Dawing on his own epeience, the autho has found that the best method to be used is the sstem appoach. This method, descibed in the pape, is pesented though the compute simulation of phsical poblems fom the sphee of the kinematics of solid bodies. To be moe specific, the solution of the poblem of the tajecto modelling of the motion of a clinde ove the edge of two planes is pesented. The solution is demonstated pogessivel it stats with the phsical and mathematical analsis of the poblem, then the algoithm development is pesented and it finishes with the pogamming in MS Ecel woksheet, though which the solution and visualization of the poblem is eached. A case stud of the sstem appoach as a suitable method of the algoithm development thinking is pesented in the pape step b step; the tet also emphasizes intedisciplina leaning of univesit students. Kewods Algoithm development, animation, intedisciplina leaning, modeling, sstem appoach. C I. INTRODUCTION OURSES in the algoithm development and pogamming ae cuentl povided in the Czech Republic at seconda schools, technical colleges and univesities in the subjects focusing on infomatics. The abilit to ceate algoithms develops logical thinking skills and imagination and is an insepaable pat of stud skills of pospective and undegaduate teaches specializing in Infomatics at the Facult of Education. Algoithms ae encounteed in all pactical activities without being ealized. An algoithm geneall involves defining the ules and giving the sequences of steps necessa fo an activities. The most common eamples of algoithms in eveda life ae vaious desciptions and giving diections. In a moe naow sense, an algoithm can be defined [1] as a pecise ule defining the pocess leading fom mutable input data up to the equied esults. Such egulations ae composed of vaious steps, stages, which ae witten in a paticula ode. A numbe of steps has to be finite. An algoithm can be undestood as an activit which consists of poblem analsis, designing phases, a method of algoithm solution and finall of compilation of the elevant algoithmic language. II. THE SYSTEM APPROACH TO THE ALGORITHM DEVELOPMENT AND PROGRAMMING Teaching of the algoithm development as well as pogamming is usuall caied out b teaches who also teach o ae close to mathematics. The issue of the algoithm development is eplained though mathematical tasks, which can be cleal descibed, defined and developed b algoithm. Altogethe, the eecises ae based on a outine ewiting of mathematical equations and fomulas using algoithms and pacticing the standad algoithm, egadless of thei compleit and sstem integation to the whole entit [5], when the eecises used ae atificial, inconsistent and disconnected fom ealit. The sstem appoach is still entiel missing in the teaching of the algoithm development and pogamming. The students who do not have sufficient mathematical epeience and knowledge do not undestand the tasks. The cannot see an inteconnection between mathematical poblems and poblems which occu in eal life. The knowledge of the algoithm development is not eached b these students; and that esults in indiffeence o esistance to the algoithm and subsequent pogamming. In ecent eas the stuctue of teaching of the algoithm development at the Univesit of Hadec Kalove has significantl moved towads the use of the sstem appoach to teaching algoithms and pogamming. This shift can be undestood as impotant pogess fo students - pospective teaches - who have to be able to appl new methods in thei wok and disseminate these new methods among seconda school students. Benefits of the new method in teaching and leaning compute science is also descibed e.g. in [], [3], [4]. The following tet will give a bief pesentation of a method fo developing of algoithmic thinking of ou students. This development should be enabled thanks to the method of the sstem appoach applied in the subject Algoithms, which contibutes to the motivation of students. Then a case stud will be pesented. It illustates a step b step modelling of a eal phsical situation as a suitable eample of an algoithmic thinking development and also as an eample of the intedisciplina sstem leaning that is useful

2 Issue 4, Volume 4, to be included in seconda school teaches education. A. Pinciples of the sstem appoach Education at seconda schools and colleges in the aea of infomatics is diected mainl to a use s attitude. Onl students who have attended optional subjects dealing with pogamming languages ae familia with ceating algoithms. Thus a lot of students studing at ou univesit lack an algoithmic knowledge at the beginning of thei studies. The sstem appoach to the poblem solution is such an appoach which undestands the studied phenomena and pocesses in comple intenal and etenal contets [6]. The sstem appoach in education consists of the fomulation, undestanding and solving the poblem, elevant pocesses, phenomena and pocesses that eist objectivel in the outside wold, and thei tansfomation into a model educational situation. The methodolog, poposed in this pape, uses fo taining of algoithms the eecises which ae based on modelling of eal and idealized phenomena, pocesses and pocedues. The methodolog is intended to lead the student to a poblem definition, to a ceation of suitable models and to implementation and ealization of the model though the pinciples of algoithms, i.e. the student should be able to detemine about the input and output data and the pocedue of the tansfomation of the data input into the data output unde the sstem appoach. B. Application of the sstem appoach The poposed new methodological appoach to teaching of algoithms can be applied: 1) In the field of sciences - in case of models of phsical and chemical pocesses and phenomena; ) In the technical field - in case of the pocess contol of machines and simple obots; 3) In the humanities and social studies - in case of the pocesses and phenomena associated with this issue; 4) In management - in case of the management pocesses and qualit contol pocesses. Mathematical calculus is essential in a model method, but onl as a seconda issue. The standad method of a simple ewiting of mathematical epessions and equations into algoithms and then into the pogams is maimall eliminated while using this appoach. It should be emphasized that the use of the sstem leaning of algoithms based on a compehensive methodological appoach can be connected with the fact that mathematics, sciences and technolog cannot do without the use of the ICT technolog; new technologies have become an integal pat. A cuent teache has to maste not onl the teaching pocess of his/he discipline, but also the foundations of the compute science. Likewise, a teache of infomatics a compute pogamme) cannot be onl a compute teache a pogamme), but s/he has to be able to sstematicall appl he/his knowledge of ICT in othe fields. The cuent non-sstematic appoach to teaching leads to such situations in which subjects ae taught in isolation, without inte-disciplina linkages. E.g. mathematical definitions, theoems and fomulas ae taught independentl; the basic pinciples of algoithms, including the development of a flowchat ae taught independentl; the basic pinciples of pogamming with emphasis on the pogamming language snta ae intepeted independentl. The education lacks a compehensive sstem appoach which would include links to e.g. phsics and phsical desciption of the eal wold. As a esult, students eceive a set of isolated findings and ules the ae unable to logicall link togethe. III. A MODEL PROBLEM SOLVED THROUGH A SYSTEM APPROACH As it was alead mentioned at the beginning of the pape, it is essential to emphasize intedisciplina leaning while taining futue teaches. This section will descibe one eal situation using intedisciplina appoaches to its solution. Simila eamples can be found e.g. in [7], [8], [9]. A. Poblem definition The situation shown in Figue 1 is to be consideed it concens an inclined plane intesecting with a hoizontal plane of angle α. Fig.1 Illustation of the given poblem A homogeneous clinde of adius olls the plane fom the left to the ight with velocit v. With espect to, v and α it has to be decided whethe the clinde olls ove the edge o ebounds fom the edge. If the clinde, unde specified conditions, ebounds, it is necessa to find a place on the inclined plane whee the clinde snaps. The situation has to be analzed on the basis of available phsical laws. Students should define the appopiate algoithm of the poblem solution and the whole situation should be animated with appopiate tools. B. Analsis of the poblem Fist, it is necessa fo the student to ealize the poblem and pefom the phsical analsis. One of the possible solutions is as follows. Let us intoduce simplifing assumptions: the olling clinde can be eplaced b a moving point mass, whose

3 Issue 4, Volume 4, position coincides with the cente of the gavit of the clinde. The cente of gavit lies on the clinde ais of the otation of the olle. The task can then be tansfeed to detemination of the tajecto of the point mass moving b speed v at the distance fom the hoizontal plane. The tajecto of the gavit cente will be epessed in the fom of =, v,, α) dependenc. On the left side above the hoizontal plane) the tajecto of the point mass is a line paallel to the plane. The distance between the plane and the line is. The situation changes when the point mass the ais of the clinde) is just above the edge whee the hoizontal plane changes in the inclined plane). At this point a student of phsics should ealize how the task has to be solved. The kinematic o dnamic solutions ae available. Both the possibilities lead to the coect solution, but the kinematic solution i.e. a non-foce solution) is simple and easie fo the algoithm development and pogamming. IV. KINEMATIC ANALYSIS The kinematic analsis of the poblem will be shown in the following pat of the pape. A. Kinematic analsis of limit cases Let us suppose, fist, that the angle of α = 0 ad. In this case, the inclined plane is hoizontal paallel to the left hoizontal plane) and the beak edge de facto does not eist. The point mass still moves at the distance fom the plane its tajecto is the line paallel with the plane). The clinde still olls. Anothe limiting situation is, if angle α = π/ ad, i.e. both the planes ae pependicula. The situation is shown in the Figue. clinde and g = 10 m/s is gavit acceleation. B eliminating time fom 1) the following fomula fo coodinate is eceived: 1 = g = 5, ) v v whee is -coodinate with the initial point at the planes edge. The clinde ebounds at the edge and neve falls back. B. Kinematic analsis of geneal cases The analsis of the situation fo the angles in the inteval α 0, π/) ad can be pesented b the following consideations. Unde cetain conditions, given b the input values and v, α and, the clinde will oll ove the edge, the clinde still holds the plane it does not ebound fom the edge). In this case, the tajecto of the point mass of the clinde at the time of olling ove the edge is a pat of the cicle. The situation is shown on the Figue 3. Fig.3 Tajecto of the clinde olling ove the edge The tajecto of the cicle is given b the equation: =. 3) Then the point mass moves along a line paallel to the inclined plane at the distance. This line can be descibed b slope intecept staight line fom: Fig. Tajecto of the clinde fo α = π/ ad In this case, the tajecto of the point mass is identical with the tajecto of the hoizontal thow and can be descibed in the [, ] coodinate sstem b the equations fo the paabola 1 = vt ; = gt, 1) whee t is time, v is velocit of the clinde, is adius of the = tg α ) +, 4) cos α whee tg α) is the slope of the line and /cos α is intecept. The oveall tajecto is composed of thee pats: the hoizontal line; the pat of the cicle; the inclined line. The tajecto can be descibed b the following fomulas:

4 Issue 4, Volume 4, ;0 : 0; sin α : C C ) = ) = sin α ; : C ) = tg α ) + cos α whee sin α indicates -coodinate of the point, whee cicle tajecto change to inclined tajecto., 5) If the clinde the point mass of the clinde) will have a sufficient velocit, the clinde will ebound fom the edge. The tajecto of the point mass fom the edge will be given b the ), the paabola ) is geometicall highe than the cicle 3) is). The tajecto of the point mass of the clinde will be a paabola up to the point the clinde impacts the inclined line, i.e. the distance of the clinde point mass equals. The oveall tajecto is composed of thee pats: the hoizontal line; the pat of the paabola see 1)); the inclined line. The tajecto can be descibed b the following fomulas: ;0 0; impact impact : ; : : P ) =, 6) P ) = 5 v P ) = tg α ) + cos α The clinde ebounds fom the edge if the tajecto of the paabola is highe than the tajecto of the cicle the values of the equation 6) ae geate than the values of the equation 5)). V. ALGORITHM DEVELOPMENT The algoithm can be developed on the basis of a phsical analsis. The algoithm allows us to build up a compute pogam suitable fo the visualization of the situation. The algoithm is based on the numeical finding of the maimum value of the equations 5) and 6) coodinate) fo the set of coodinate. If the maimum is given b 5), the clinde olls ove the edge, if the maimum is given b 6), the clinde ebounds fom the edge. A. Input and output data To build an algoithm, it is necessa to define the input data - this means the speed of the clinde v, the adius of the clinde and the angle between the hoizontal and inclined planes α. The simplest fom of the output is, whethe the ebound occus o not vaiable of the Boolean tpe); and if it does, then what the -coodinate of the impact on the inclined plane is. B. Desciption of the algoithm The final algoithm of the solution given in the fom of the flowchat is pesented in Figue 5. whee impact indicates -coodinate of the impact point and is given b the solution of the equation fo : 5 = tg α ) +. 7) v cos α The situation is shown in Figue 4. Fig.4 Tajecto of the clinde ebound fom the edge The clinde olls ove the edge if the tajecto of the cicle is highe than the tajecto of the paabola the values of the equation 5) ae geate than the values of the equation 6)). Fig.5 The algoithm of the poblem solution

5 Issue 4, Volume 4, The algoithm is based on gaduall step b step compaison of value of C given b 4) and P given b 5) calculated fo a sufficientl small inceases in the coodinates. That means using a ccle with a finite numbe of epetitions and conditions. In this paticula case the inteval of 0,15 is split to 00 pats with incease d = This algoithm can be ewitten in an pogamming language, e.g. in the algoithmic meta-language, as in [3]. begin ead, v, α) Rebound := False; I := 0; while I <= 00 do begin X := I * 0.075; Yc := f C X,,v,a) Yp := f P X,,v,a) if Yc < Yp then begin Rebound := Tue; Ximpact := X; end; I := I + 1; end; wite Rebound, Ximpact); end. Howeve, students can also consequentl each the esults using MS Ecel and then the can pactice the wok with this envionment. VI. SOLVING THE PROBLEM USING MS EXCEL The task can be also easil demonstated using fomulas enteed in the MS Ecel speadsheet cells. This solution, given b a wide negotiabilit of MS Ecel, appeas to be the most advantageous. Anothe eason to use MS Ecel is that students should be accustomed to using a pogamming tool as simple as possible. In the following pat of the pape thee will be shown how vaious elements of the algoithm inputs, outputs, ccle, conditions) can be ewitten b commands diectl in an Ecel woksheet, and how to ceate a simple animation chat. A. Inputs and Outputs The input and output data in the Ecel woksheet ae conducted diectl into the cells. The cells should be coloumaked to indicate that those ae the significant cells. In ou paticula case, the algoithm input values, v and α ae enteed into cells H, H3 and H4, the output data into cells H6, H7. B. Ccle Vaious steps of the ccle defined b the numbe of epetitions can be implemented fo each step of the ccle to be epesented b diffeent cells of one column. The fomulas of the ccle ae enteed in cells A, B and B3 and then, dagging the handle of the cells, copied into an numbe of cells using elative addessing of the cells). The numbe of the copied cells coesponds to the total numbe of the epetitions of the ccle. A possible solution is shown in Figue 6. The inteval of the solution is fo the values of taken fom 0 to +15, this inteval is divided into 00 pats, which coesponds to the numbe of steps of the ccle of the algoithm flowchat. The incement d is Fig.6 Solution of the poblem in MS Ecel Speadsheet The set of values X is in column A. The values of Y C given b 5) ae in the column B. The values of Y P given b 6) ae in the column C. C. Conditions Column D contains a condition that compaes the coesponding values in columns B and C. The fomula in e.g. ow 3 has following epession: =IFC3>B3;1;0). In the case that at least one of the values of column B is bigge than the coesponding values in the cells of column C which is identified b 1) the clinde will ebound fom the edge. This is one of the outputs given in cell H6. The fomula in this cell has following epession: =IFSUMD:D0)>0;"YES";"NO"), The output is YES if the summation of values in the column D is geate than 1, othewise the output is NO. The last value in the cells of column C which is bigge than that in the coesponding cells of column B last value 1 in column D) appoimatel detemined the coodinate of the impact point. To detemine this point the following function is inseted in the cells of the column E: =IFANDD3=1;D4=0);A3;""). This condition compaes if the coesponding cell of the column D equals 1 and the following one equals 0. If the condition is fulfilled the coesponding value fom cell of column A, which indicates -coodinate of impact point, is copied. This value is also copied to cells H7 as the second output.

6 Issue 4, Volume 4, VII. VISUALIZATION OF THE PROBLEM This section will demonstate how the given situation can be elativel simpl and effectivel visualized while using MS Ecel. Based on the animation of the clinde motion along the calculated tajecto, the visualization is ceated. A. Animation Animation geneall means a wa how a static image can be seemingl set in motion. The pinciple of an animation is ecoding of a sequence of images which slightl diffe. Duing a quick viewing of subsequent images an impession of movement occus, due to the phenomenon of the pesistence of vision. The fequenc of changing of individual images is popotional to the displacement of the object in consecutive images. The bigge the displacement of objects in each image is, the geate the fequenc of changing these images must be to maintain a sense of motion). Animations of the clinde motion can be ealized b using an XY scatte chat. The chat itself does not change, howeve, onl the position of the lines on the chat changes. The chat shows both the static baselines and the dnamic animated objects. The static baselines epesent the hoizontal inclined plane and the tajecto of the clinde cente the point mass epesenting the clinde). The line epesenting the tajecto on the left side fom the edge is hoizontal in distance fom the hoizontal plane. On the ight side fom the edge thee ae lines which epesent both tajectoies given b 5) and 6). The above lines do not change duing the animation, the ae static. Dnamic objects which move on the chat with espect to static baselines ae illustated b a point, which epesents the clinde cente, and the cicle, which epesents the edge of the cicle see Figue 7. Fig.7 Static baselines and dnamic objects The pinciple of the animation of the scatte chat in MS Ecel is based on the change of one o moe paametes of the chats input data of the dnamic objects the clinde cente and the cicle). The objects step b step change its position in elation to the static baselines. In this paticula case one paamete coodinate of the clinde cente - will be step b step changed b a athe small incement d. A change of this paamete can be achieved b using so-called iteative calculation of values in the cell. Othe vaiables needed fo the animation of the dnamic objects depends on this coodinate and the ae ecalculated diectl in the Ecel woksheet. B. Iteation In geneal, iteation means epetition of cetain activities - the wod comes fom the Latin iteetu - epeat. The iteation in mathematics and numeical methods is a pocess of appling a function f epeatedl, using the output value n+1 of the function as input agument n of the function in the net step. This can be witten b mathematical fomula n+ 1 = f n ). 8) A tpical eample of the use of iteations is the numeical solution of nonlinea equations b the geneal iteative method - see e.g. [10]. A tpical eample of a nonlinea equation is the tanscendental equation = cos. 9) To find the appoimate solution, one has to popel set the initial value of e.g. 0 = 1), to povide the iteation i + 1 = cos i ) and to see how the value of is changing. The temination of the iteations is detemined b the equied accuac - ε. The calculation will be teminated if the following condition is fulfilled: 1 < ε. 10) i + i Apat fom solving of the nonlinea equations, the iteation calculus can be used e.g. fo detemination of values of ecusivel given sequences. As mentioned e.g. in [4] o [8] the sequences ae defined eithe b eplicit fomulas fo the n-th tems o ecusivel which means that the pevious values of tems of the sequence ae used to geneate the value of the net tem of the sequence. In othe wods one needs to know the initial value 0 and the ecuence constuction to be able to find subsequent tems of the sequence. Let us biefl emind a basic mathematical fomulation of ecusivel defined sequences. Given a eal function f: N 0 R R and an initial value 0 R, conside the sequence of iteates of 0 unde the given function f: 0 1 3, = = = f f f 0, 0 ), 0, 1 ), 0, ),. 11) Such a sequence is called a ecusivel defined sequence. It means that fo a given 0, we can compute an abita tem of sequence t, whee t = 0, 1,,, accoding to the elation t + 1 = f 0, t ),. 1) This elation, togethe with an initial value 0 is called a fist

7 Issue 4, Volume 4, ode ecuence equation. The solution to this equation is an sequence t geneated b this equation. The temination condition in the case of ecuentl given sequences is given b numbe of sequence tems t ma. Eample of such sequence can be sequence given b following fomula: t 0 t + 1 ma = 0, = t = 5 + with the tems 0,, 4, 6, 8. C. Iteation in algoithm development and pogamming 13) Iteation in algoithm development and pogamming means a epeated call of the function wheeas the agument of the function is the esult of the pevious function call. In this sense, the iteation coesponds to the afoementioned case of ecusivel given sequences. The iteation in algoithm development and pogamming is theefoe called ecusion. An impotant pat of ecusion is a teminating condition which detemines when the ecusion is to be stopped. The ecusion in pogamming is quite often used, as well as e.g. the assignment statement A:=A+ can be undestood as a fom of ecusion based on 13) with the numbe of epetition t ma = 1. This epession means that the new vaiable value equals to the oiginal value inceased b. D. Iteation /ecusion in the MS Ecel The cicula efeence can occu in the fomula of the cell in the Ecel sheet. This means that the fomula in a cell efes to the value of the same cell, eventuall that the fomula of the cell efes to the value of anothe cell, which has a fomula linking back to the oiginal cell. Fig. 9 Setting of iteative calculation paametes in MS Ecel The item Maimum Iteations specifies the maimum numbe of iteations, epetitions, which Ecel povides in an iteative calculation. The item Maimum Change sets the accuac of the iteative calculation - the value of the cell befoe and afte the iteation is compaed. If the absolute diffeence of the both values is smalle than the accuac of the calculation, the iteation is stopped. The default value of Maimum Iteations is set to 100 and the default value of Maimum Change is set to The iteative calculation and its temination can be epessed in the fom of the algoithm flowchat in Figue 10, whee the following vaiables ae used: NI - the numbe of the alead done iteations; X old - the value of the cell befoe the iteation; X new - the value of the cell afte the iteation; MI - the maimum iteations; MC - the maimum change. Fig. 8 Eamples of cicula efeence in MS Ecel The value of such cells can be detemined onl b the iteative calculation. If such an iteative calculation is not possible in MS Ecel option tools default is disabled), the calculation will be eecuted and an eo message will be shown. The iteative calculation in vesion of MS Ecel 007 can be enabled in the Ecel Options dialog bo which is eached b clicking to the Ecel option button in the main menu) in the folde Fomulas see Figue 9. The Enable iteative calculation checkbo has to be checked. Fig. 10 Flowchat of iteative calculation in MS Ecel It is clea that the teminating condition is given eithe b the maimum of iteations 13) o b condition 10). E. Setting of iteative calculation fo an animated chat In the following passage it will be shown how to use the iteative calculation in animated chats. Specificall, as it has been mentioned above, the iteative calculation will be used to

8 Issue 4, Volume 4, change the -coodinate of the cente of the clinde. The value of this paamete is enteed in cell X3. The cicula efeence fomula =X3+W3, is enteed into cell X3. This fomula epesses that the value of cell X3 afte one iteative ecalculation step inceases b the incement value enteed in cell W3 - iteation animation) step. Iteative ecalculation stats b pessing of F9 ke. The numbe of the iteation steps is set b the value of Maimum Iteations. To make onl one step of the iteation, defined b fomula in cell X3, the value of Maimum Iteations has to be equal to 1, as is evident fom the Figue 9. B epeated pessings, eventuall b holding down the ke F9, the value of cell X3 will step b step incease b the value of the animation step value in cell W3. If onl the fomula =X3+W3 was enteed to the cell X3, the value of X3 would afte each iteation step still incease. It is theefoe necessa to detemine the teminating condition, i.e. minimum and maimum limits, given b the values in the cells U3, V3 espectivel, so that onl within this inteval the value of cell X3 will incease. This can be done b adding the following condition to fomula in cell X3: =IFX3>=V3,U3,X3+W3). This condition compaes the value in cell X3 with the value in cell E3. If the condition is tue X3 V3) the value of X3 changes to the minimum given b value in cell U3. Othewise, the iteative calculation is caied out and the value of X3 cells inceases b the value of the iteation step value of the cell W3). The situation is shown on the Figue 11. ecalculated using the fomulas 5) and 6). The fomulas ae enteed to cell Y3. F. Animation of movement of clinde in XY scatte chat The above mentioned pinciple of the iteative ecalculation of the and coodinates of the clinde cente can be advantageousl used as a base fo ceation of an animated chat. MS Ecel speadsheet has implemented tools fo ceation of gaphs. These tools allow uses to ceate diffeent tpes of chats, and among othes, e.g. a XY scatte chat, which allows to pesent a set of [, ] points with given coodinates and in the plane. A diffeent tpe of the cuve can also be plotted in this chat, if the sufficient numbe of the [, ] points foming the cuve is used. In this case, on the chat the ae shown both the static baselines the hoizontal plane, the inclined plane and the tajecto of the clinde cente given b equations 4) and 5)) and the moving objects the point epesenting the clinde cente and a cicle aound this cente, showing the suface of the clinde). The coodinates of the clinde cente [ c, c ]) ae given b values in the cells X3 and Y3, espectivel. The values of the set of the points [, ] needed fo dawing of the cicle depend on the coodinates of the clinde cente [ c, c ]) b following fomulas: = c + cos α, 14) = + sin α c whee α is the angle, the change is fom 0 to 360 with incement 5. This set of points is also ecalculated duing each step of the iteation of cell X3. The solution in MS Ecel is shown in Figue 11. The esult of the above mentioned is this: when the F9 ke is epeatedl pessed o held, the cente of the clinde and a cicle dum suface) move fom the left to the ight on the chat and the chat appeas as animated. Figue 1 shows the XY scatte chat, ceated diectl using the Ecel tools, of the tajectoies of the mass point fo values = 5, v = 10 and α = 30. Fig. 11 Solution of the iteative calculation of the clinde cente and cicle coodinates The iteative ecalculation of the above defined paamete coodinate of the clinde cente will be within the ange fom a minimum value value of the cell U3) to a maimum value value of the cell V3) with the iteation step the value of the cell W3) b epeated pessings o b holding of ke F9. Within this inteval, the cente of clinde will move fom left to ight in the XY scatte chat. Simultaneousl, the -coodinate of the clinde cente is Fig. 1 XY scatte chat of the solution in MS Ecel gaph tool

9 Issue 4, Volume 4, VIII. CONCLUSION Thee ae vaious appoaches how to povide taining in algoithms, how to intoduce and develop basic algoithmic thinking of students. A new kind of the teaching / leaning stateg using the sstem appoach was pesented in the pape. Algoithms as the geneal basis of a stuctued poblem solving can be undestood as the basis of the compute science. The fomation of the stuctue of the poblem in sepaate steps develops ceative thinking while appling a sstem appoach to diffeent tpes of poblems. The pape emphasizes the fact that the algoithm is neithe a mee mathematics, no a mee pogamming. The sstem appoach can be set as the default paadigm fo a wide integation of the pinciples of the algoithm development into education. ACKNOWLEDGMENT This eseach has been patiall suppoted b the Specific eseach poject of the Facult of Science of Univesit of Hadec Kalove No. 19. REFERENCES [1] A.A. Makov, Theo of algoithms, Moscow: Impint, [] E. Milkova, Multimedia Applications and thei Benefit fo Teaching and Leaning at Univesities, WSEAS Tans. on Infomation Science & Applications, Issue 6, vol. 5, June 008, pp [3] E. Milkova, Algoithms: The Base of Pogamming Skills, in Poc. 9th Intenational Confeences on Infomation Technolog Inte- Faces, Univesit of Zageb, Coatia, 007, pp [4] P. Pazak, Recusivel Defined Sequences and CAS, in Poc. 6th WSEAS/IASME Intenational Confeence on Educational Technologies EDUTE 10), WSEAS Pess, Kantoui, Sousse, Tunisia, 010, pp [5] B. Wilson, Soft Sstems Methodolog: Conceptual Model Building and its Contibution. Hoboken: Wile, 001. [6] W. Dettme, The Logical Thinking Pocess: A Sstems Appoach to Comple Poblem Solving, Visconsin: Qualit Pess, 007. [7] S. Hubalovsk, E. Milkova, Modelling of a eal situation as a method of the algoithmic thinking development, in Poc. 6th WSEAS/IASME Intenational Confeence on Educational Technologies EDUTE 10), WSEAS Pess, Kantoui, Sousse, Tunisia, 010, pp [8] S. Hubalovsk, E. Milkova, P. Pazak, Modeling of a Real Situation as a Method of the Algoithmic Thinking Development and Recusivel Given Sequences, WSEAS Tans. on Infomation Science & Applications, Issue 8, vol. 7, Aug. 010, pp [9] S. Hubalovsk. Use of application MS Ecel fo calculation of the gavit cente of a sstem of ight paallelepipeds. Mathematics, phsics, infomatics, vol. 19, 010, pp in Czech) [10] V. Jehlicka, Numeical methods, Solution of non-linea equations [Online] Available: In Czech). Stepan Hubalovsk was bon in Tutnov, Czech Republic in 1970, he obtained maste degee in education of mathematics, phsics and compute science in 1995 and docto degee in theo of education in phsics in 1998 both in Facult of Mathematics and Phsics, Chales univesit in Pague, Czech Republic. He woked 5 eas as maste of mathematics, phsics and compute science on seveal seconda schools. He woks as assistant pofesso on Univesit of Hadec Kalove fom 006. He inteested in algoithm development, pogamming and compute modelling. RND. Stepan Hubalovsk, Ph.D. is membe of Union of Czech Mathematicians and Phsicist.