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Text of the page (random words):
plete program under the name to appear shortly as a mooc on edx digimat will be launched as a new mathematics education for school university related to the fenics project as a open source platform för automatic mathematical simulations digimat will from this platform successively be transformed to a new platform see also swedish version digimat is based on the principle that all mathematical objects are constructed computed through the execution of av computer programs construction of the natural numbers 1 2 3 by repetition of the basic operation of 1 construction of integers by repetion of 1 construction of rational numbers as pairs of integers construction the operations of addition subtraction multiplication och division on natural and rational numbers construction of straight line plane coordinate system construction of spatial representation in coordinate systems of geometrical objects straight line circle rectangle triangle construction of motion of geometrical objects in coordinate systems constructiv calculus as time stepping of dx v dt constructive mechanics and physics by calculus constructive matematickl modeleing of systems in physics chemistry economics construction of computer games as interactive mathematical modeling all previous games in codea on this site can more or less directly be transferred into javascript as contributions to games workshop polynomials on november 7 2018 by claes johnson leave a comment construction of polynomials by time stepping dx i x i 1 dt var x var q var f var t var dt var n function setup n 5 t 0 dt 0 01 for var i 0 i n i x i 0 x 0 1 createcanvas 400 400 function draw t t dt for var i 1 i n i x i x i x i 1 dt q i i x i x i 1 nostroke fill 0 ellipse 50 40 t 350 10 x i 3 3 fill 255 0 0 255 ellipse 50 40 t 355 10 q i 3 3 fill 0 0 255 255 ellipse 50 40 t 355 10 pow t i factorial i 3 3 fill 0 255 0 255 ellipse 50 40 t 350 10 x 0 3 3 stroke 0 line 50 350 350 350 line 50 350 50 50 fill 0 text construction of polynomials x t t n n 100 50 text by time stepping dx i x i 1 dt 100 70 text black x i t 100 100 text blue pow t i factorial i 100 150 text red i x i t x i 1 t vs t black 100 200 text green x 0 t 1 100 250 function factorial n if n 0 n 1 return 1 if f n 0 return f n return f n factorial n 1 n logarithm dx dt t on november 7 2018 by claes johnson leave a comment logarithm dx 1 t dt var x 0 var t 1 var dt 0 01 function setup createcanvas 400 400 function draw time stepping t t dt x x dt t output fill 0 stroke 0 line 50 350 350 350 line 50 350 50 50 line 50 350 350 50 text logarithm x log t red 200 50 text exponential x exp t green 200 100 text compare dx dt t with dt tdx 200 150 text t axis 360 350 text x axis 40 40 fill 255 0 0 255 nostroke ellipse t 20 50 350 x 50 2 2 fill 0 255 0 255 nostroke ellipse x 50 50 350 t 20 2 2 exponential dx x dt on november 7 2018 by claes johnson leave a comment exponential dx x dt var x 1 var t 0 var dt 0 01 function setup createcanvas 400 400 function draw time stepping t t dt 10 x x x dt output fill 0 stroke 0 line 50 350 350 350 line 50 350 50 50 text exponential x t exp t 200 50 text t axis 360 350 text x axis 40 40 fill 255 0 0 255 nostroke ellipse t 5 50 350 x 2 2 binary multiplication by 2 on november 7 2018 november 7 2018 by claes johnson leave a comment binary multiplication by 2 var bit var bitnew var i 5 var d 1 var n function setup n 1 for var i 0 i i 1 i bit i floor random 0 2 bitnew i 0 createcanvas 400 400 function draw background 220 fill 0 text number of digits 20 20 text a digit can be 0 or 1 20 40 text click to multiply by 2 250 20 text binary multiplication 2 150 390 text i 120 20 text pow 2 n 1 370 20 the addition operator for var i 0 i i 1 i if bit i d bit i 1 bit i 1 1 bit i 0 output if bit 0 1 fill 0 255 0 255 ellipse 305 80 10 10 fill 0 255 0 255 for var i 0 i 1 i ellipse 305 110 10 i 5 5 if bit 1 1 fill 255 255 0 255 ellipse 305 40 80 10 10 fill 0 255 0 255 for var i 0 i 2 i ellipse 305 40 110 10 i 5 5 if bit 2 1 fill 255 0 0 255 ellipse 305 80 80 10 10 fill 0 255 0 255 for var i 0 i 4 i ellipse 305 80 110 10 i 5 5 if bit 3 1 fill 0 0 255 255 ellipse 305 120 80 10 10 fill 0 255 0 255 for var i 0 i 8 i ellipse 305 120 110 10 i 5 5 for var i 0 i 8 i ellipse 305 120 110 10 i 5 5 if bit 4 1 fill 0 ellipse 305 160 80 10 10 fill 0 255 0 255 for var i 0 i 16 i ellipse 305 160 110 10 i 5 5 for var i 0 i i i fill 0 text bit i 300 40 i 100 10 fill 0 255 0 255 ellipse 100 300 10 10 ellipse 150 300 10 10 fill 0 text 120 302 20 text 170 302 20 fill 255 255 0 255 ellipse 200 300 10 10 fill 255 255 0 255 ellipse 100 320 10 10 ellipse 150 320 10 10 fill 0 text 120 322 20 text 170 322 20 fill 255 0 0 255 ellipse 200 320 10 10 fill 255 0 0 255 ellipse 100 340 10 10 ellipse 150 340 10 10 fill 0 text 120 342 20 text 170 342 20 fill 0 0 255 255 ellipse 200 340 10 10 fill 0 0 255 255 ellipse 100 360 10 10 ellipse 150 360 10 10 fill 0 text 120 362 20 text 170 362 20 fill 0 0 0 255 ellipse 200 360 10 10 function mousepressed for i 0 i i 1 i bitnew i 1 bit i for i 0 i i i bit i bitnew i n n 1 binary subtraction 1 on november 7 2018 november 7 2018 by claes johnson leave a comment binary subtraction click var bit var i 5 var d 1 var n var n1 function setup n 32 for var i 0 i i i bit i 1 createcanvas 400 400 function draw background 220 fill 0 text number of digits 20 20 text a digit can be 0 or 1 20 40 text click to subtract 250 20 text binary subtraction 1 150 390 text i 120 20 text n 1 360 10 the subtraction operator for var i 0 i i 1 i if bit i 0 bit i 1 bit i 1 1 bit i 1 output if bit 0 1 fill 0 255 0 255 ellipse 305 80 10 10 fill 0 255 0 255 for var i 0 i 1 i ellipse 305 110 10 i 5 5 if bit 1 1 fill 255 255 0 255 ellipse 305 40 80 10 10 fill 0 255 0 255 for var i 0 i 2 i ellipse 305 40 110 10 i 5 5 if bit 2 1 fill 255 0 0 255 ellipse 305 80 80 10 10 fill 0 255 0 255 for var i 0 i 4 i ellipse 305 80 110 10 i 5 5 if bit 3 1 fill 0 0 255 255 ellipse 305 120 80 10 10 fill 0 255 0 255 for var i 0 i 8 i ellipse 305 120 110 10 i 5 5 if bit 4 1 fill 0 ellipse 305 160 80 10 10 fill 0 255 0 255 for var i 0 i 16 i ellipse 305 160 110 10 i 5 5 for var i 0 i i i fill 0 text bit i 300 40 i 100 10 for var i 0 i n 1 i fill 0 255 0 255 ellipse 365 20 10 i 5 5 fill 0 255 0 255 ellipse 100 300 10 10 ellipse 150 300 10 10 fill 0 text 120 302 20 text 170 302 20 fill 255 255 0 255 ellipse 200 300 10 10 fill 255 255 0 255 ellipse 100 320 10 10 ellipse 150 320 10 10 fill 0 text 120 322 20 text 170 322 20 fill 255 0 0 255 ellipse 200 320 10 10 fill 255 0 0 255 ellipse 100 340 10 10 ellipse 150 340 10 10 fill 0 text 120 342 20 text 170 342 20 fill 0 0 255 255 ellipse 200 340 10 10 fill 0 0 255 255 ellipse 100 360 10 10 ellipse 150 360 10 10 fill 0 text 120 362 20 text 170 362 20 fill 0 0 0 255 ellipse 200 360 10 10 function mousepressed bit 0 bit 0 1 n n 1 gravitating bodies on november 5 2018 november 14 2018 by claes johnson leave a comment here is a new start with javascript using the p5 js editor particle system under gravitational attraction click var x var dx var vx var fx var y var dy var vy var fy var m var dt var n var i var r function setup createcanvas 400 400 n 100 i 1 dt 0 001 for var i 0 i n i x i random 1 200 x 0 200 dx 0 fx 0 vx i random 100 100 y i random 1 200 y 0 200 dy 0 fy 0 vy i random 100 100 m i random 5 20 m 0 10 r 0 function draw background 0 0 0 5 fill 0 0 255 255 text particle system under gravitational attraction 100 50 fill 255 0 0 255 text click to add new mass and follow dynamics 100 70 for var i 0 i i i fx 0 fy 0 for var j 0 j i j dx x i x j dy y i y j r pow dx 2 pow dy 2 r sqrt r fx fx m i m j 1000000 dx pow r 10 3 fy fy m i m j 1000000 dy pow r 10 3 vx i vx i fx dt m i vy i vy i fy dt m i x i x i vx i dt y i y i vy i dt fill 20 i 40 i 255 20 i fill random 0 255 random 0 255 random 0 255 255 nostroke ellipse x i y i m i m i function mousepressed x i mousex y i mousey i i 1 binary addition 1 on november 3 2018 november 7 2018 by claes johnson leave a comment binary numbers add 1 click the same thing with base 3 here is an intro to binary numbers with position system supported by color var bit var i 5 var d 1 var n function setup n 1 for var i 0 i i i bit i 0 createcanvas 400 400 function draw background 220 fill 0 text number of digits 20 20 text a digit can be 0 or 1 20 40 text click to add 1 250 20 text i 120 20 the addition operator for var i 0 i i 1 i if bit i d bit i 1 bit i 1 1 bit i 0 output if bit 0 1 fill 0 255 0 255 ellipse 305 80 10 10 fill 0 255 0 255 for var i 0 i 1 i ellipse 305 110 10 i 5 5 if bit 1 1 fill 255 255 0 255 ellipse 305 40 80 10 10 fill 0 255 0 255 for var i 0 i 2 i ellipse 305 40 110 10 i 5 5 if bit 2 1 fill 255 0 0 255 ellipse 305 80 80 10 10 fill 0 255 0 255 for var i 0 i 4 i ellipse 305 80 110 10 i 5 5 if bit 3 1 fill 0 0 255 255 ellipse 305 120 80 10 10 fill 0 255 0 255 for var i 0 i 8 i ellipse 305 120 110 10 i 5 5 for var i 0 i 8 i ellipse 305 120 110 10 i 5 5 if bit 4 1 fill 0 ellipse 305 160 80 10 10 fill 0 255 0 255 for var i 0 i 16 i ellipse 305 160 110 10 i 5 5 for var i 0 i i i fill 0 text bit i 300 40 i 100 10 for var i 0 i n 1 i fill 0 255 0 255 ellipse 365 20 10 i 5 5 fill 0 255 0 255 ellipse 100 300 10 10 ellipse 150 300 10 10 fill 0 text 120 302 20 text 170 302 20 fill 255 255 0 255 ellipse 200 300 10 10 fill 255 255 0 255 ellipse 100 320 10 10 ellipse 150 320 10 10 fill 0 text 120 322 20 text 170 322 20 fill 255 0 0 255 ellipse 200 320 10 10 fill 255 0 0 255 ellipse 100 340 10 10 ellipse 150 340 10 10 fill 0 text 120 342 20 text 170 342 20 fill 0 0 255 255 ellipse 200 340 10 10 fill 0 0 255 255 ellipse 100 360 10 10 ellipse 150 360 10 10 fill 0 text 120 362 20 text 170 362 20 fill 0 0 0 255 ellipse 200 360 10 10 print bit 0 function mousepressed bit 0 bit 0 1 n n 1 mathematics it as newmath on april 6 2016 april 30 2016 by claes johnson leave a comment newmath mathematics it is a basic school version of the bodyandsoul university mathematics education reform program the swedish version is presented at matematik it mathematics it combines the language of mathematics with programming and the computational power of the computer into a new tool for simulation of real and imagined worlds to be used to understand and handle these worlds mathematics it is constructive mathematics where all mathematical objects are constructed computationally all of this can be described as different forms of computer games where the student both constructs programs and plays the game where computer game means interaction between player and mathematical model using the computational power of the computer the main questions are here what can i construct how do i do to construct such a thing rather than the traditional questions what am i supposed to do how am i supposed to do that the questions and answers are here connected so that how influences what the perspective is thus open towards a large variety of different constructive possibilities for different students rather than closed as in traditional school mathematics towards few possibilities the same for everybody the question why has a different answer when possibilities are many than when possibilities are few mathematics it is below presented as a sequence of computer games in posts game1 game2 game3 from the simplest to more complex where the design and programming of the game is the main point we use codea which is a user friendly app for programming on the ipad for the ipad mathematics it is supported by a set of apps on app store illustrating different basic concepts and serving as inspiration for student work on programming apps for app store and can be found searching for new math take a look and see that these apps serving the basic school version also represent central core of bodyandsoul for university newmath mathematics it thus offers a mathematics education with a new uniformity over levels where the basic questions are the same independent of level what can be computed and how apps on app store on april 5 2016 may 6 2016 by claes johnson leave a comment mathematics it is supported by a number of apps on app store with the dual purpose of illustrating basic concepts of mathematics and programming and serving as inspiration for student work to create apps on app store here are the icons of some of the apps here are the links counting mechanics1 mechanics2 pythagoras calculus1 calculus2 biology1 atoms dark energy piano secret running1 crash model tacoma bridge elastic body bird swarm dynamics andree north pole expedition posts navigation older posts search for search recent posts new start polynomials logarithm dx dt t exponential dx x dt binary multiplication by 2 binary subtraction 1 gravitating bodies binary addition 1 mathematics it as newmath apps on app store constructive mathematics programming game1 natural numbers base 10 game2 natural numbers base 2 game3 angrymathbirds easy game4 natural numbers game5 elementary functions game6 2d geometry game7 flight simulator easy game8 planetary systems game9 squareroot of 2 game10 derivative and integral game11 foxes and rabbits game12 battle between the colors game13 vibrating string game14 sinus cosinus and pi game15 exponential functional exp t and e game16 trampoline game17 systems of bodies and springs game18 elastic chain game19 collison game20 bungy jump game21 racing game22 atoms game23 flume ride game24 molecule dance game25 elastic body game26 steering by wheel or force game27 insect invasion game28 multi pendulum game29 many balls game30 bouncing ball on springy support game31 pin ball game game32 balance control game33 angrymathbirds windmill game34 rally game35 swing vs resonant forcing game36 binary graphical representation game37 binary graphical calculator game38 binary addition game39 binary multiplication game40 bit dating game41 binary division game42 binary numbers and physics game43 animation game44 100m dash game45 build tower and count game46 physics engine game47 marathon game48 binary counting for kindergarten game49 big crunch game50 andrées expedition the story game51 text to speak input game52 jumping ape game 53 bird flocking recent comments christopher hoen on game35 swing vs resonant archives november 2018 april 2016 march 2016 february 2016 january 2016 other cj blogs cj on mathematics and science matematik it the world as computation mathematical simulation technology the secret of flight computational blackbody radiation categories uncategorized search for search recent posts new start polynomials logarithm dx dt t exponential dx x dt binary multiplication by 2 recent comments christopher hoen on game35 swing vs resonant archives november 2018 april 2016 march 2016 february 2016 january 2016 categories uncategorized blog at wordpress com subscribe subscribed leibniz world of math sign me up already have a wordpress com account log in now privacy leibniz world of math subscribe subscribed sign up log in report this 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