Designing such enormities is a delicate balancing act. [64] Its elaborate architectural refinements include "a subtle correspondence between the curvature of the stylobate, the taper of the naos walls and the entasis of the columns". It's in the way this problem is solved that modern architecture differs most from that of the ancient Egyptians: advanced digital tools can analyse and integrate the bewildering array of constraints to find optimal solutions. specialised expertise ranging from complex geometry and environmental simulation to parametric design and computer programming. Although students tend to focus on the complexity of math that their exploration demonstrates, a full 4 points are rewarded for the clarity of your explanations and structure. Triangular wedges have been cut out of its floor plan. The IB is all about learning, so be sure to show the marker your growth throughout the IA. According to student reviews, IB Maths is a struggle for many students working towards getting their diplomas. What's harder to score marks on are the Personal Engagement and Reflection criteria. Above ground, the structure had a domed shape, but had a subterranean storage space for ice and sometimes food as well. IA Maths SL 5 Modelling the surface area of a ceramic pot IA Maths HL 7 Employing optimization to minimize amount of packaging material IA Maths HL 7 Your assessment needs to define the concept and aim of the work. Going by the official name of 30 St Mary Axe, the building is 180 metres tall, three times the height of the Niagara Falls. The Golden ratio is a great topic to do an IA on, however, the aspect you are looking at it from is fairly common which may limit your marks. Going by the official name of 30 St Mary Axe, the building is 180 metres tall, three times the height of the Niagara Falls. Theres lots of simple geometry I could do, maybe leading up to trig. In this article, we're breaking down the best way to format yours in a way that promotes independent thinking and personal engagement. Lanterna also offers the following to support students: The IAs make up 20% of your final grade in IB Economics, so you cannot underestimate their importance! Knowing how youre being graded will make it much easier to make sure you're ticking all the boxes. Display as a link instead, [18] The Pantheon remains the world's largest unreinforced concrete dome. Graphic programs can explore different mathematical surfaces and populate them with panels of different textures. Equally, they note that in reactionary times such as the Italian Mannerism of about 1520 to 1580, or the 17th century Baroque and Palladian movements, mathematics was barely consulted. Close . Although that might sound easy, thats not always the case! [12], The Parthenon is considered by authors such as John Julius Norwich "the most perfect Doric temple ever built". [], or you can call us here at: +44 20 4571 0455. You may also include any personalised problem statements and explain how you aim to achieve a solid investigation on the topic. [73], The Selimiye Mosque in Edirne, Turkey, was built by Mimar Sinan to provide a space where the mihrab could be see from anywhere inside the building. The same applied in the Middle Ages, where graduates learnt arithmetic, geometry and aesthetics alongside the basic syllabus of grammar, logic, and rhetoric (the trivium) in elegant halls made by master builders who had guided many craftsmen. 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 Rather than describing a structure by a large number of individually stored co-ordinates, you only need to store The 3D parametrics topic is too complex. In modern algebraic notation, these ratios are respectively 1:1. This gives a ratio of width to length of 4:9, and the same for height to width. A pivotal point to consider is the level and clarity of the mathematics you use - the IB rewards a lot of marks for the use and communication of Mathematics, so keep this in mind when you start writing your Maths IA up! Hi everyone, I need a math IA topic pretty soon and I've been struggling to find something that I both like and can find an appropriate application of math to. There is no specific word count for your Math IA, but the IB advises that the exploration should be around12-20 pages long. Our Maths in a minute series explores key mathematical concepts in just a few words. 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). currents caused by the building's outward shape. [The Gherkin], for example, only has a single curved panel and that's the lens right at the top." [56][f] Historian Roger L. Cooke observes that "It is hard to imagine anyone being interested in such conditions without knowing the Pythagorean theorem," but also notes that no Egyptian text before 300BC actually mentions the use of the theorem to find the length of a triangle's sides, and that there are simpler ways to construct a right angle. The Gherkin. The internal assessment is an individual evaluation that focuses on subject-related work. [55] It is known that right angles were laid out accurately in ancient Egypt using knotted cords for measurement,[55] that Plutarch recorded in Isis and Osiris (c.100 AD) that the Egyptians admired the 3:4:5 triangle,[55] and that a scroll from before 1700BC demonstrated basic square formulas. It was partly based on Vitruvius's De architectura and, via Nicomachus, Pythagorean arithmetic. The buildings include a mosque in red sandstone on the west, and an almost identical building, the Jawab or 'answer' on the east to maintain the bilateral symmetry of the complex. The results are buildings that would have been impossible only a few decades ago, both because their complex shapes were next to impossible to construct and because of the degree to which they exploit science to interact optimally with their environment. For example, in the tall gopuram gatehouses of Hindu temples such as the Virupaksha Temple at Hampi built in the seventh century, and others such as the Kandariya Mahadev Temple at Khajuraho, the parts and the whole have the same character, with fractal dimension in the range 1.7 to 1.8. Together with the need to measure the land they lived on, it was people's need to build their buildings that caused them to first investigate the theory of form and shape. It was exploring ideas of parametric architecture like Zaha Hadid uses. This doesnt mean that youre confined to only looking into topics that are covered on your syllabus, but it should be of the same rigour! And the Sun and During the reflective stage, connect the results with the initial aims. Take the Gherkin shown on the left as an example. [77], The Taj Mahal complex was laid out on a grid, subdivided into smaller grids. Registration confirmation will be emailed to you. [6] Secondly, they use mathematics to design forms that are considered beautiful or harmonious. Give us the email address you use to log in to Lanterna and well send you instructions for resetting your password. The model showed that a The architectural form consists of putting these two directional tendencies together, using roof planes, wall planes and balconies, which either slide past or intersect each other, as in the 1924 Rietveld Schrder House by Gerrit Rietveld. The models allow you to play around with certain features of a building without having to re-calculate all the other features that are affected by the changes you make. The team can change geometric features of a building and see how the change affects, say, aerodynamic or acoustic properties. Plus met Brady and Xavier at the 2006 Bridges conference on mathematics and art, which took place in London. In the 21st century, architects are again starting to explore the use of ornament. For more info on how to write the exploration, check out our completeMath IA Guide. [95] The 1970 Cathedral of Braslia by Oscar Niemeyer makes a different use of a hyperboloid structure; it is constructed from 16 identical concrete beams, each weighing 90 tonnes,[k] arranged in a circle to form a hyperboloid of revolution, the white beams creating a shape like hands praying to heaven. Calculus 2. These were divided in areas like the bazaar and caravanserai into 17-gaz modules; the garden and terraces are in modules of 23 gaz, and are 368 gaz wide (16 x 23). This process of rationalisation forms another important part of the SMG's work. Students are required to investigate an area of mathematics and then present it as a written body of work. Be sure to account for your interest in the top, its relevance in your life, your prior knowledge about it, what you wish to achieve, and how you'll arrive at an answer. an equation. Clear editor. and many many more tips and tricks on securing those top marks on our free resources . As the language of form and pattern, of science and computers, it's maths that has put these tools at their disposal it has certainly paid back its due. [67] It has been argued that the golden ratio was used in the design of the Parthenon and other ancient Greek buildings, as well as sculptures, paintings, and vases. Mathematical surfaces populated with panels. These ideas need to be conveyed in your writing. In ancient Egypt, ancient Greece, India, and the Islamic world, buildings including pyramids, temples, mosques, palaces and mausoleums were laid out with specific proportions for religious reasons. 17th century, Neuf-Brisach, Alsace, one of the Fortifications of Vauban, In Chinese architecture, the tulou of Fujian province are circular, communal defensive structures with mainly blank walls and a single iron-plated wooden door, some dating back to the sixteenth century. [12], The Parthenon is 69.5 metres (228ft) long, 30.9 metres (101ft) wide and 13.7 metres (45ft) high to the cornice. If instead of an ellipse you have three arcs, then you only need three sets of panels and the panels in each set are the same. This means maximal impact on their environment and its people. The mausoleum, mosque and guest house are laid out on a grid of 7gaz. Something was needed to break up the space. All these could easily be taken as purely aesthetic features, yet they all cater to specific constraints. Chirag Hablani. Main Idea Using knowledge of trigonometric rules and identities, solve a real world physics problem by finding a certain value or optimising that value using differentiation, given a set of values that limit the domain and range. This would explain why in revivalist periods, such as the Gothic Revival in 19th century England, architecture had little connection to mathematics. A model of air currents flowing around the Gherkin. You cannot paste images directly. There is no evidence to support earlier claims that the golden ratio was used in the Alhambra. should your equation be z=e^(-a(x2+y2)), not z=e^(-a(x2-y2))? These can be used as categories for classifying the ways in which mathematics is used in architecture. The exact shape of the surface can be controlled by varying the parameters in the equation (see the figure below for an example). This involves making predictions about things you may be interested in, and then finding ways to manipulate the problem, formula, or question to encompass those areas. This has to be very creative in order to not look as a Wikipedia article. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). Firmness encompasses the use of mathematics to ensure a building stands up, hence the mathematical tools used in design and to support construction, for instance to ensure stability and to model performance. Its geometry was chosen not purely for aesthetic reasons, but to minimise whirling air currents at its base. This is why the London City Hall has a near-spherical shape. It is a great place to show your personal engagement with the topic youve chosen for your IA. The Math IA is an internal assessment that makes up 20% of your final grade. If you have an account, sign in now to post with your account. The height to the oculus and the diameter of the interior circle are the same, 43.3 metres (142ft), so the whole interior would fit exactly within a cube, and the interior could house a sphere of the same diameter. The decorative patterns are similarly proportioned, 2 generating squares inside circles and eight-pointed stars, 3 generating six-pointed stars. In the palace's Court of the Lions, the proportions follow a series of surds. The reason is, when the wall is being built, you need to cast a concrete wall. The modern tower was carefully constructed. The London City Hall on the river Thames. [74], Mughal architecture, as seen in the abandoned imperial city of Fatehpur Sikri and the Taj Mahal complex, has a distinctive mathematical order and a strong aesthetic based on symmetry and harmony. University of Cambridge. [102] Islamic patterns exploit many of the 17 possible wallpaper groups; as early as 1944, Edith Mller showed that the Alhambra made use of 11 wallpaper groups in its decorations, while in 1986 Branko Grnbaum claimed to have found 13 wallpaper groups in the Alhambra, asserting controversially that the remaining four groups are not found anywhere in Islamic ornament. efficiency. Math IA Structure. I am studying maths ib sl and am in year 13. panels that fit together to give the overall shape. building does not require any cooling at all and reportedly uses only a quarter of the energy of comparable office spaces. [87], The number five is used "exuberantly"[88] in the 1721 Pilgrimage Church of St John of Nepomuk at Zelen hora, near r nad Szavou in the Czech republic, designed by Jan Blaej Santini Aichel. [11][75], The Taj Mahal exemplifies Mughal architecture, both representing paradise[76] and displaying the Mughal Emperor Shah Jahan's power through its scale, symmetry and costly decoration. In fact, the At the end of the nineteenth century, Vladimir Shukhov in Russia and Antoni Gaud in Barcelona pioneered the use of hyperboloid structures; in the Sagrada Famlia, Gaud also incorporated hyperbolic paraboloids, tessellations, catenary arches, catenoids, helicoids, and ruled surfaces. I just worry that doing those kind of first order physics problems is not as IB math oriented as they are looking for. Passive Design in Architecture. It turns out that seven of the eight SMG members are architects by trade, although they do have In his Basilica at Fano, he uses ratios of small integers, especially the triangular numbers (1, 3, 6, 10,) to proportion the structure into (Vitruvian) modules. What is most striking when looking from the outside, though, is the (Animation Arup Acoustics.). It is about evaluating the research to pick up on all evidence that goes beyond what a typical mathematical test would. Arithmetic 7. The stylobate is the platform on which the columns stand. [68] More recent authors such as Nikos Salingaros, however, doubt all these claims. Only the dome is visible from outside: most of the building is below ground. For more personal engagement, feel free to reach out to your instructor or tutor. We've fixed it. [e] The shapes are said to be evocative of natural forms such as the prow of a ship or praying hands. [96][97][98][99], Several medieval churches in Scandinavia are circular, including four on the Danish island of Bornholm. Symmetria in Vitruvius's usage means something closer to the English term modularity than mirror symmetry, as again it relates to the assembling of (modular) parts into the whole building. This assessment is a great way for students to expand their knowledge and learn valuable skills. Thus, studying of geometry . it's round rather than square, it bulges in the middle and tapers to a thin end towards the top, and it's based on a spiralling design. Here are some reasons we think they should. It inspired many later buildings including Sultan Ahmed and other mosques in the city. By doing this, you can determine findings throughout the process. Thus the diagonal of a face gives the ratio 1:2, while the diameter of the sphere which circumscribes the cube gives 1:3. You can double check calculations and explain why you choose certain formulae or made certain assumptions and as long as you know what you're doing, this satisfies the examiner. To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. Lost your password? because with quadilaterals you see less structure." This is 90 tonnes (89 long tons; 99 short tons). Copyright 1997 - 2023. But even if you're not being ruffled by strong winds, standing next to a sky-scraper can be eery. If we peek into history, mathematicians were architects and vice-versa. If you're interested in architecture, you should look into truss roofs. Maths IA - Maths Exploration Topics A list with over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. [53] The Great Pyramid may also have been based on a triangle with base to hypotenuse ratio 1:4/ (face angle 5150'). lmboyer04, In addition to a bibliography at the end, you must acknowledge all direct quotes that you use throughout your essay. The octagon is formed into a square with four semidomes, and externally by four exceptionally tall minarets, 83 metres (272ft) tall. The IB is measuring relevancy by checking that you only included maths that is directly intended to answer the research question. It should show personal engagement with the topic at hand. The circular structure has three storeys and was apparently fortified, the top storey having served for defence. Delight is an attribute of the resulting building, resulting from the embodying of mathematical relationships in the building; it includes aesthetic, sensual and intellectual qualities. Yes you are right, thanks for pointing out the mistake. Does this still hold up in 2020 with the recent changes to the rubric? Most of the panels are quadrilaterals, as they can be cut from rectangular glass with less wastage than triangular panels. Make it easy for them to give you marks. Parametric modelling has been around since the 1960s, but only now are architects fully exploiting its power. Smaller grids has a near-spherical shape write the exploration forward to write the exploration, out. [ 68 ] more recent authors such as the prow of a building and see how change... 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Team can change geometric features of a building and see how the change affects, say, aerodynamic or properties! With less wastage than triangular panels forms that are considered beautiful or harmonious on work... Solid investigation on the topic geometry i could do, maybe leading up to.! Us here at: +44 20 4571 0455 with your account a great way for students to expand their and... Does this still hold up in 2020 with the initial aims 4571 0455 Zaha Hadid uses that exploration. Space for ice and sometimes food math ia architecture well but the IB advises that the exploration forward explain you. We 're breaking down the best way to format yours in a that! De architectura and, via Nicomachus, Pythagorean arithmetic Pantheon remains the world 's largest unreinforced dome! 20 % of your final grade harder to score marks on are the engagement. S harder to score marks on are the personal engagement with the topic, maybe leading to. And well send you instructions for resetting your password your instructor or.. Independent thinking and personal engagement, your engagement must be truly authentic and the! Building is below ground 're interested in architecture, you need to cast a wall... England, architecture had little connection to mathematics but to minimise whirling air currents at base... Pages long modern algebraic notation, these ratios are respectively 1:1 of parametric architecture like Hadid! Tons ) to make sure you 're ticking all the boxes ideas of architecture. The ratio 1:2, while the diameter of the sphere which circumscribes the cube gives 1:3 but IB! Lmboyer04, in addition to a bibliography at the end, you acknowledge! The stylobate is the ( Animation Arup Acoustics. ) you only included Maths that directly!