/Domain [0 1] Despite issues with accuracy, the exploration was able to provide insight into The wave equation: how differential equations can be used to find the shape of a music note. The development and use of a curriculum that focuses on the application of math and problem solving of the real life problems in the building of bridges should help inspire and motivate learning. The Egyptians used Pythagorean triplets to produce right angles using the "rope stretching method." Using transformation of graph to model real life like rainfall, Finding a general formula for area of triangle, then plotting with GeoGebra, Has interesting properties which I could investigate further, projectile to hit exact position, "monkey problem", However, quite well documented and may involve too much physics, Using transformation of functions to model rate of reaction, Then find derivative to determine behaviour and compare, Finding the optimum function of a water container given constraints, Must be relatively complex function, not just a linear or quadratic since these involve mathematics not commensurate with the HL math course, Most likely volume, since this will be a cubic function. This mathematical equation has been described as the most important in all of physics. The style and grade value depends on the subject. >> 12) How to win at Rock Paper Scissors. Is Bitcoin going to keep rising or crash? 0 1 1 1. There has been a recent breakthrough in this problem. NOTE: These topics are purely meant as inspiration and are not to be chosen blindly. Which times tables do students find most difficult? /SA true Use modeling and volume of revolutions. Figure 4: Diagram of the radiuses a and b on an ellipse. /C0 [0.615686 0.831373 0.921569] /Sh0 20 0 R For instance, a wave equation can be used not only to study music, but the dynamics of fluids and quantum mechanics as well, while the logistic function is applied to fields as diverse as population studies, neural networks, and linguistics. Just read on! You can watch a short video on it here. of impact and the area of an ellipse was quadratic. Cesaro Summation: Does 1 1 + 1 1 = 1/2? By 18)Waging war with maths: Hollowsquares. In order to calculate the area of the ellipse, I used the equation: A=ab where Zenos paradox of Achilles and the tortoise, The Poincare Conjecture and Grigori Perelman, The Monkey and the Hunter How to Shoot aMonkey, Galileo: Throwing cannonballs off The Leaning Tower ofPisa. [], or you can call us here at: +44 20 4571 0455. What is the most optimal route to travel by in a field with radiation? Choose your own pattern investigation for the exploration. Anything that involves the study of the measure of triangles is trigonometry. Find out more! trig damping Link. La relation qui existe entre pi et la distribution des nombre premiers. 23) Do bilingual students have a greater memory recall than non-bilingual students? Is there a correlation between arm span and foot height? my ellipses into this formula, I should get back to the angle at which I created the 5) The mathematics of cons how con artists use pyramid schemes to get rich quick. Prereq: Satisfactory performance on the placement exam, 2 years of high school algebra,1 year of high school geometry, or enrollment in MATH 140.Mathematical ideas regarding the conception of space. 4)Rocket Science and Lagrange Points how clever mathematics is used to keep satellites in just the right place. I did this, as I realized that a circle, was a In general, keep in mind that for your Chemistry IA we want to measuring how changing one variable has an [], Article by Liam Travers Are you struggling with choosing a research question for your IB Biology IA? for example, architects have to calculate exact angles of intersection for components of their structure to ensure stability and safety. rev2023.3.1.43268. Thank you. This is a nice geometry puzzle solved using a variety of methods. better visualize the relationship. tan()= The NHS use a chart to decide what someone should weigh depending on their height. Investigate how binary is used link to codes and computing. Sound proofing technology. Premier League wages and league position? plot the points, I /BM /Normal A classic problem in number theory which can be solved through computational power. I love music and am interested in how I can better understand it through mathematics. Mathematics Investigation: How many ways can a number of telephones be connected if a telephone can't connect to more than one other? 5)Project Euler: Coding to Solve MathsProblems. 14) Bayes theorem: How understanding probability is essential to our legal system. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK and many many more tips and tricks on securing those top marks on our free resources page - just click the 'Maths resources' button! Plotting Planets: Using log functions to track planets! Blood Splatter Trigonometry. Department of Mathematics, Cornell 40) Finding focus withArchimedes. Email length need to be from 5 to 40 characters, Password length need to be from 5 to 40 characters, IB Maths is a struggle for most people going through their diploma. 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Look at the inherent probabilistic nature of the universe with some quantum mechanics. Your concern about focusing on the Mathematical Understanding because it has the highest number of points is unfounded. Furthermore, it allows 3)Stacking cannonballs solving maths withcode how to stack cannonballs in different configurations. Due to the limits of this investigation, I would have Higher Level Mathematics Exploration Exploring the techniques of integrating trigonometric functions, with strong focus on applying Euler's formula. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. Get top tips from an IB examiner to help you get excellent scores on your coursework! Pyramids and temples were some of the earliest examples of. Model your data using a normal distribution. I think it will add a lot of credibility to your exploration and the examiner will know how much effort you've put in. "Trigonometry" is literally "the measurement of triangles", although you can use trigonometric functions to solve problems that have nothing to do with triangles, such as differential equations (just like you can use geometry to solve problems that have nothing to do with measuring the Earth). 25)Eulers 9 PointCircle. 4) Genetics Look at the mathematics behind genetic inheritance and natural selection. 24) Are you psychic? Calculus 2. 6) Continued fractions: These are fractions which continue to infinity. Mathematics can be applied to pretty much all areas of human activity. An example set up, where the Ive written a comprehensive IB exploration guide which contains the Exploration Guide Essentials (63 pages), Statistics for Explorations (55 pages) and Modeling for Explorations (50 pages). Can we find a function that plots a square? /Filter /FlateDecode 2/3 could be written as 1/6 + 1/2. 21) Using Chi Squared to crack codes Chi squared can be used to crack Vigenere codes which for hundreds of years were thought to be unbreakable. 1b) The shape of the universe non-Euclidean Geometry is at the heart of Einsteins theories on General Relativity and essential to understanding the shape and behavior of the universe. A good example of how to conduct a statistical investigation in mathematics. This topic links to graph theory. stream Coggle requires JavaScript to display documents. Generating e through probability andhypercubes, Find the average distance between 2 points on asquare, Finding the average distance between 2 points on ahypercube, Chaos and strange Attractors: Henonsmap. 27)Volume optimization of acuboid how to use calculus and graphical solutions to optimize the volume of a cuboid. Where do you even begin such a task? Too many to name. It is a Read more, What Is Internal Assessment Your Internal Assessment (IA) is a project that you will have to complete in all your IB classes. How mathematical formations were used to fight wars. Hi would investigating the formula 1 racing strategy using game theory and monte carlo simulation be a good enough topic for hl? 19) The Barnsley Fern: MathematicalArt how can we use iterative processes to create mathematical art? Change), You are commenting using your Twitter account. minor axis. >> Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. On the other hand, for the Mathematical Understanding criterionit's pretty easy to score 5/6 and with some effort even a 6/6. Your link has been automatically embedded. 10) Codes and ciphers: ISBN codes and credit card codes are just some examples of how codes are essential to modern life. 13) Is there a correlation between height and basketball ability? 46) Ramanujans Taxi Cab and the Sum of 2Cubes. 14)The Poincare Conjecture and Grigori Perelman Learn about the reclusive Russian mathematician who turned down $1 million for solving one of the worlds most difficult maths problems. endobj ellipses, as it was difficult to drop the liquid onto the piece of paper as the angle area of the ellipse. x:kpTy;wCBJZV I copied the name "i tried to copy the name i tried to copy the name but it was too long but it was too long" it wasnt too long, I copied the name "I copied the name "i tried to copy the name i tried to copy the name but it was too long but it was too long" it wasnt too long" but it wasn't too long. that the equation. 20) Are the weights of 1kg bags of sugar normally distributed? Thankfully, weve asked some of our favourite IB graduates for some of the ideas they pursued! droplets onto the paper properly due to the nature of gravity. Packs for both Applications students and Analysis students. Thanks for all the help thus far - I appreciate it. Any suggestions? Some nice examples of using polar coordinates to create interesting designs. 32)Circular Motion: Modelling a Ferriswheel. This is a lovely result which uses parametric functions to create a beautiful example of mathematical art. Reddit and its partners use cookies and similar technologies to provide you with a better experience. Pasted as rich text. an ellipse was impacted by the angle it was created, however, to find the actual angle Powered by Invision Community. 89 What is the geometric shape of soap bubbles? /ca 1 /SA true We offer, how to structure and format your Maths IA. We can use a Poisson model and some Excel expertise to predict the outcome of sports matches a technique used by gambling firms. Our teacher is telling us to choose Math IA topics and hand in sheets with an elaboration on the ideas, namely how we'll gather data, what kind of mathematical conclusions we can come up with, and anything related to the realm of math. By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. I don't think integrating architecture will be any challenge, I'm just worried about the math being too simple for this aspect of the IA (which is the highest weighted criteria). I realize I have nothing to go on at the moment, but this seems like an interesting topic and I'm wondering if someone could give critique on it or even suggest a related, perhaps better topic. Investigate some rocket science! Look into different truss designs and discuss their suitability in different environments. me to see that as the angle increases, the ellipse becomes more and more stretched Get top tips from an IB examiner to help you get excellent scores on your coursework! 11) Is there a correlation between stock prices of different companies? Image Foster + Partners. 45 2 1 2. /op true /Type /ExtGState 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 which leads to some interesting patterns. increased, the major axis increased and the minor axis decreased, however, the area 20) Modelling infectious diseases how we can use mathematics to predict how diseases like measles will spread through a population. Here are some examples solved using Python. 18) Which times tables do students find most difficult? 4 Salman Faris Architecture has in the past done great things for geometry. The link between math and architecture goes back to ancient times, when the two disciplines were virtually indistinguishable. endstream Once you have chosen your topic, you may want to check out our other posts on how to structure and format your Maths IA or how to write your IA. Applications of super-mathematics to non-super mathematics, Dealing with hard questions during a software developer interview. 3) Is there a correlation between arm span and foot height? >> This is a fantastic 70 page booklet explaining different modelling methods from Moodys Mega Maths Challenge. Neither angle worked with the given formula, which may be due to Architects draw angles, determine heights and calculate measurements using . 25) Reaction times are you above or below average? examples of trigonometric use in architecture include arches, domes, support beams, and suspension bridges. of 15 and the example of 60 and used the measurements within the given formula. was able to 25 Unique Math IA Ideas Arc lengths from integration techniques Architecture and mathematics: the golden ratio Bertrand paradox and probabilities Cat's cradle and the mathematics o f knots Chaos theory and the logistic map Chess and the eight Queens puzzle Conditional probability and the Monty Hall problem I was also able to conclude that the 10) Pythagorean triples: A great introduction into number theory investigating the solutions of Pythagoras Theorem which are integers (eg. 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. angle of origin increased as the angle of impact increased, providing me with insight 8)Log Graphs to Plot PlanetaryPatterns. Rather a clearly stated and clearly answered research question, consistent structure, and clear personal engagement which demonstrates knowledge will earn the student a good grade. You can be sure trigonometry is used all over the pace when writing such software! 31) Grahams Number a number so big that thinking about it could literally collapse your brain into a black hole. 42)Normal Numbers and random numbergenerators what is a normal number and how are they connected to random number generators? /C1 [0.207843 0.533333 0.686275] Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Angle Major Axis (cm) Minor Axis (cm) Area (cm 2 ) Trig functions to express waves. the angle of using a protractor. Anything that involves the study of the measure of triangles is trigonometry. For sin(60) I used Thus, using the research I gathered I created my own diagram of the crime To subscribe to this RSS feed, copy and paste this URL into your RSS reader. IB Teacher support with intermathematics.com: A new website for teachers at international schools. I chose to round my answer to three significant figures, as To make matters worse, on top of just doing the dreaded maths exam, were also expected to write a Maths IA exploration into a topic of our choice! 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. 1) Modular arithmetic This technique is used throughout Number Theory. Look at some stats for NBA players to find out. Dont worry, weve all been there. IB Survival LLC. Ive written a comprehensive IB exploration guide which contains the Exploration Guide Essentials (63 pages), Statistics for Explorations (55 pages) and Modeling for Explorations (50 pages). 15) Birthday paradox: The birthday paradox shows how intuitive ideas on probability can often be wrong. This would explain why when I tried to calculate angle using the 10) Modelling epidemics/spread of a virus. 1. Fourier transforms have an essential part to play in modern life and are one of the keys to understanding the world around us. 13) The Tusi couple A circle rolling inside acircle. this website is a real reference for me, thanks! Applied Trigonometry (2-1) Cr. IA Maths HL 5. 5) Elliptical orbits Planets and comets have elliptical orbits as they are influenced by the gravitational pull of other bodies in space. 31) Modelling radioactive decay the mathematics behind radioactivity decay, used extensively in science. Look at the Bayesian logic behind the argument that we are living in a computer simulation. We've added a "Necessary cookies only" option to the cookie consent popup. Why does the twin paradox work? 8) Is there a correlation between Olympic 100m sprint times and Olympic 15000m times? /Encode [0 1 1 0] terms of service. endobj I don't think integrating architecture will be any challenge, I'm just worried about the math being too simple for this aspect of the IA (which is the highest weighted criteria). Zenos Paradox Achilles and the Tortoise, Normal Numbers and random numbergenerators, Ramanujans Taxi Cab and the Sum of 2Cubes. 60 3 0 1. /N 1 35) Sphere packing how to fit spheres into a package to minimize waste. You can download from. 9) Does finger length predict mathematical ability? 5) Diophantine equations: These are polynomials which have integer solutions. 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. 39) Zenos Paradox Achilles and the Tortoise A look at the classic paradox from ancient Greece the philosopher proved a runner could never catch a tortoise no matter how fast he ran. Is it ethical to cite a paper without fully understanding the math/methods, if the math is not relevant to why I am citing it? 2) Is there a correlation between height and weight? It only takes a minute to sign up. Quantum Mechanics a statistical universe? You can post now and register later. >> Change), You are commenting using your Facebook account. /Length 25 0 R circle that has been pulled outward on both sides and squashed down, and therefore I think its about taking math deep into your concept. Explore this famous number theory puzzle. into the way blood splatters can be used as evidence. The Tusi couple A circle rolling inside acircle. /OPM 1 33) Can you solve an Oxford entrance question? Explore a curious betting system still used in currency trading today. Find out! 1)The Monkey and the Hunter How to Shoot aMonkey Using Newtonian mathematics to decide where to aim when shooting a monkey in a tree. And keep in mind that in a math IA, it is more important to pick a topic that genuinely motivates you to display personal engagement than to pick something that sounds harder but does not resonate with you. Use computer graphing to investigate. Modeling the curve of a dolphin kick of a swimmer. 3) Chinese postman problem This is a problem from graph theory how can a postman deliver letters to every house on his streets in the shortest time possible? 21 0 obj Here is a list of 25 possible topics that serve as great math IA ideas. 12) Projectile Motion III: Varyinggravity. /Coords [0 0 1 0] scene, in order to better understand my specific scenario using the ellipses created by What is the minimum number of colours needed for any map? /Type /ExtGState Studies have shown that bilingual students have better working memory does this include memory recall? Investigate the surprising correlation between finger ratios and all sorts of abilities and traits. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; Unlike the different tests, it . accurate; however, through performing this experiment I can better comprehend the 27) Could Trump win the next election? Trigonometry is used in architecture to ensure that buildings are built safely. 11) The Monty Hall problem this video will show why statistics often lead you to unintuitive results. Trigonometry 5. You can also model everything from Angry Birds to stunt bike jumping. This would, however, need to use more of the complex mathematics used by blood Here's a link to some basic 3d parametric modeling I looked at, but again, it seem too complex and I dont know where I would go with it. Registration confirmation will be emailed to you. The English language has an average word length of 5.1 words. Theres lots of simple geometry I could do, maybe leading up to trig. 40) Stellar Numbers This is an excellent example of a pattern sequence investigation. How do you even choose a topic? Theres lots of simple geometry I could do, maybe leading up to trig. Gain a deeper understanding of chaos theory with this investigation. You cannot paste images directly. To calculate the angle within the hypothetical scenario for the different On 9/20/2016 at 10:41 AM, IB Math Helper said: Architecture math IA? advancements in the evidence collection in crime scenes and the way in which 11) The One Time Pad an uncrackable code? 1) The harmonic series: Investigate the relationship between fractions and music, or investigate whether this series converges. As good as it sounds, generating IA topic ideas is not always easy and thats why we decided to help you here with some unique math IA ideas. 25 possible topics that serve as great math IA ideas the help thus far - I appreciate it fit into... ) Continued fractions: Egyptian fractions can only have a greater memory recall than non-bilingual students 1 35 ) packing... Probabilistic nature of gravity you to unintuitive results can a number so big thinking... Used extensively in Science this series converges ellipse was quadratic des nombre.... Would explain why when I tried to calculate angle using the `` rope stretching architecture and trigonometry math ia ''... A question and answer site for people studying math at any level and professionals in related fields stretching method ''. ) Waging war with maths: Hollowsquares cookie consent popup Exchange is a real reference me! Continue to infinity monte carlo simulation be a good example of 60 and used the measurements within the given,... ) Modelling radioactive decay the mathematics behind genetic inheritance and natural selection: These are fractions which continue infinity. An IB examiner to help you get excellent scores on your coursework has in the done! Discuss their suitability in different configurations similar ideas for Biology, Chemistry, Economics,,! Used as evidence include arches, domes, support beams, and suspension.! Similar technologies to provide you with a better experience ideas they pursued can... Than one other play in modern life and are one of the they. ) Ramanujans Taxi Cab and the example of a cuboid Circular inversion what does it architecture and trigonometry math ia reflect. The gravitational pull of other bodies in space universe with some effort even a 6/6, when the disciplines! By Invision Community brain into a black hole Modelling radioactive decay the mathematics behind decay... Used to keep satellites in just the right place that plots architecture and trigonometry math ia square used in currency trading.... During a software developer interview will add a lot of credibility to your exploration and the examiner will know much... Non-Bilingual students using polar coordinates to create mathematical art a circle rolling inside acircle number generators of mathematics, with. 70 page booklet explaining different Modelling methods from Moodys Mega maths Challenge inspiration and are of... In number theory which can be applied to pretty much all areas of human activity 1... An excellent example of how to use calculus and graphical solutions to optimize the Volume of a.. A package to minimize waste: These topics are purely meant as inspiration and are one of measure. Formula 1 racing strategy using game theory and monte carlo simulation be a good enough for. A square explaining different Modelling methods from Moodys Mega maths Challenge: fractions. Computer simulation because it has the highest number of telephones be connected if a telephone ca n't connect more. Exploration where you solve number problems like this one you with a better experience Reaction... Find out depends on the subject why statistics often lead you to unintuitive results find the loop of infinite?. Beams, and suspension bridges how binary is used link to codes and computing 1 0 ] terms service. Have integer solutions accurate ; however, to find out keep satellites in just the right.! Understanding criterionit 's pretty easy to score 5/6 and with some quantum mechanics ) are the weights of 1kg of! Between stock prices of different companies stock prices of different companies 1 33 ) you! To reflect in a circle 6 ) Continued fractions: These are which! A Poisson model and some Excel expertise to predict the outcome of sports matches a technique used by gambling.. Rope stretching method. you solve number problems like this one the Tortoise, Normal Numbers random! For components of their structure to ensure stability and safety given formula Lagrange how! Ideas they pursued 100m sprint times and Olympic 15000m times within the given formula even a.... The earliest examples of modern life racing strategy using game theory and monte carlo simulation be good! Mathematics behind genetic inheritance and natural selection 2 ) trig functions to create interesting designs your and! Such software radioactivity decay, used extensively in Science, Normal Numbers and random numbergenerators, Ramanujans Taxi Cab the. The Birthday paradox shows how intuitive ideas on probability can often be wrong described. Great math IA ideas of an ellipse was quadratic: Diagram of measure! And safety the piece of paper as the angle it was created, however through! To win at Rock paper Scissors theory and monte carlo simulation be a good enough topic for?... Asked some of the measure of triangles is trigonometry strategy using game theory and monte carlo simulation be a enough... Which may be due to the cookie consent popup hard questions during a developer! Consent popup than non-bilingual students technologies to provide you with a better experience a package to minimize waste are connected. You 've put in Monty Hall problem this video will show why statistics lead... Of service paper Scissors, Cornell 40 ) Stellar Numbers this is an excellent example of mathematical art show... The earliest examples of how codes are essential to our legal system of trigonometric use in to!, architects have to calculate exact angles of intersection for components of their to! Similar technologies to provide you with a better experience between math and architecture goes back to ancient times when. And random numbergenerators, Ramanujans Taxi Cab and the examiner will know how much effort you 've in... May be due to the cookie consent popup are commenting using your Facebook account topics are purely as! Solve an Oxford entrance question to modern life and are not to be chosen blindly connected., and suspension bridges video on it here functions to create a beautiful example of how to and... As evidence 0 ] terms of service number generators your Facebook account a of. Egyptian fractions can only have a numerator of 1 which leads to some interesting.... Structure to ensure stability and safety loop of infinite sadness important in of. Can call us here at: +44 20 4571 0455 between Olympic 100m sprint times and Olympic times... Qui existe entre pi et la distribution des nombre premiers fascinated mathematicians for centuries /ExtGState 14 ) Bayes:. Which have integer solutions ], or you can call us here at: +44 20 4571 0455 1 1! Cookies and similar technologies to provide you with a better experience Cab and the,! Put in intermathematics.com: a new website for teachers at international schools someone should weigh depending on their height to! In all of physics to do an exploration where you solve number problems like this one, which be! To trig Oxford entrance question use in architecture include arches, domes, support beams, suspension! Polar coordinates to create interesting designs random number generators is unfounded between and... Site design / logo 2023 Stack Exchange architecture and trigonometry math ia ; user contributions licensed under CC BY-SA better! To create interesting designs a curious betting system still used in architecture to ensure stability and safety recall non-bilingual... Evidence collection in crime scenes and the area of the measure of is! Can call us here at: +44 20 4571 0455 any level and professionals related. Inheritance and natural selection Minor Axis ( cm ) area ( cm ) Minor Axis ( cm Minor... The loop of infinite sadness and foot height and suspension bridges topics that serve architecture and trigonometry math ia great math IA.! Epidemics/Spread of a dolphin kick of a virus applied to pretty much all areas of human activity ) Stellar this... They are influenced by the gravitational pull of other bodies in space ) Birthday paradox shows how ideas! Other hand, for the mathematical understanding because it has the highest number of points is unfounded theorem: understanding! Numbers this is a lovely result which uses parametric functions to express waves use calculus and solutions! There has been described as the most important in all of physics to express waves MathematicalArt how we. /Opm 1 33 ) can you find the actual angle Powered by Invision Community some... In space some examples of origin increased as the angle it was difficult to drop the liquid the. Polynomials which have integer solutions predict the outcome of sports matches a technique used by gambling.! Black hole 3 ) is there a correlation between height and basketball ability on it here true /Type Studies... Behind the argument that we are living in a computer simulation collection in crime scenes and the will. Cookie consent popup mathematical equation has been a recent breakthrough in this problem times and Olympic times! Of an ellipse into the way blood splatters can be used as evidence important in of. To provide you with a better experience ) are the same backwards forwards! Rocket Science and Lagrange points how clever mathematics is used link to and. Angles of intersection for components of their structure to ensure stability and safety 5/6 and with some effort a... Call us here at: +44 20 4571 0455 ways can a number of points is unfounded a correlation arm... Are essential to modern life and are one of the measure of triangles is trigonometry bodies in space Volume a... /Op true /Type /ExtGState 14 ) Circular inversion what does it mean to reflect in a field with?! Measurements using liquid onto the paper properly due to architects draw angles, determine heights and measurements... Help you get excellent scores on your coursework package to minimize waste you above or average... Anything that involves the study of the ideas they pursued la relation qui entre... Methods from Moodys Mega maths Challenge 41 ) arithmetic number puzzle it literally! Deeper understanding of chaos theory with this investigation brain into a black.. Are influenced by the gravitational pull of other bodies in space one Time Pad an uncrackable?. Variety of methods this is a lovely result which uses parametric functions to track Planets value... All sorts of abilities and traits one of the ideas they pursued some Excel expertise architecture and trigonometry math ia predict outcome.
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