Read "Conceptual Mathematics A First Introduction to Categories" by F. William Lawvere available from Rakuten Kobo. In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathem...
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Type: Design Workshop Name: Structural Modelling Year: 2019 Supervisor: Eike Schling Office: The University of Hong Kong, Department of Architecture The workshop on modular structures produced beautiful and divers results of construction a doubly curved structure from repetitive pieces.
“GRIB 4” (Bernar Venet Studio)Mathematics and art may seem irrelevant in the world of contemporary art, in which artistic creativity takes precedence over the aesthetic ideals pursued by Renaissance artists. But French artist Bernar Venet said mathematics has inspired his works since the early 1960s, when he started his career as an artist. The first painting Venet created was a mathematical painting that resembles functional graphs consisting of symmetrical curves on a y-axis. “I painted a line
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Tricks like the butterfly method in fractions should be avoided. What happens if we add three or more fractions? Instead, focus on conceptual understanding.
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Description ...look above at Fig. 4! It may seem a bit intimidating at first, but that's just because of the numbers and extra dots. In the previous examples, as well as the floor on page 2VP 9, everything was equally spaced apart, because everything was equal in size. But if you want to draw, say, a city- real-world or even fantasy- it is unlikely that a block of buildings will be equal in size to streets and alleys. What do you do? The first thing you must do is decide on a "key" object. This is sort of a reference point for everything else, since everything usually exists in relation to everything else. In this case, I started this the same way as before- I drew that square on the 45 degree line, right on the bottom line, just as before. That is my reference. Once again I have points A and B. Once again I measured their distance from point C, which I'm calling "Center" here. No reason, really- guess it was pretty late... Now, if I had continued as before, I would have had something similar to Fig. 2- everything the same distance away, and the same size. But THIS time, I wanted the "streets" between the dark squares to be 1/2 as wide as they would normally be. So- between A and Center, right in the middle if them, I drew in a new point, point "1." Between B and Center I did the same with point "2." I then connected point 1 to vanishing point 1, and point 2 to vanishing point 2. Already you can see a more narrow strip than before. Helpful Hint: When doing this, in this way, at NO TIME should any line from either vanishing EVER go through any of the dark squares. Now, here you have to imagine what you want: something similar to the previous examples, but with more narrow strips between the squares- but on all sides of any square there will be squares. Just like before. By now you have narrow strips right next to the first square, left and right. You want it to be a full strip, so- draw in points on the bottom line, each that 1/2 of A-to-Center (or 1/2 B-to-Center), and connect the next dots to the appropriate vanishing points- in this case, the point to the left of A to VP 2, and the point to the right of B to VP 1. Now you have one dark square, and two narrow strips. Now connect those same points to the other vanishing points- that is why they are numbered "1,2." Slowly, connecting each point to the vanishing points indicated, leaving out the ones in parenthesis for now, observe how the picture develops: as the lines criss-cross, more squares among the narrow strips. Your best bet is to move outward from the center, one at a time, left, then right. Since I wanted a white border, I also left out the ones with an "*" under them. Darken in the squares and you have it. The whole key here is deciding how much more narrow- or wider!- you wnat those "streets." It could have been 1/4 as wide, or 2 1/2 times as wide- and you base the measurements on Center, A, and B. Since, as earlier in this tutorial, the square is the basis for cubes, pyramids, and more, what would happen if we expand on this some more? Bring in...Fig. 5! This is just what we have in Fig. 4, only I built up blocks (I didn't bother to make perfect cubes, just "buildings") in the usual way, with vertical lines. Leaving some squares alone, making a small pit with one, and varying the sizes a bit, keeping in mind which blocks out what (as with any such picture), look at the streets and alleys between the buildings. Oh- I just sort of threw in the wall opposite the border. It gives that sliding block a nice view of things, no? If you had wanted those squares to be the TOPS of the buildings, instead of the bases, you could have drawn vertical lines DOWNWARD, again keeping in mind which would block out what. You could even have used a third vanishing point, too (to have used it for Fig. 5, either you'd have to shrink the original squares, or expand the new ones on top of the buildings). I did this one a just a couple of days ago- and it was the first time I was actually able to do it without guessing. Have fun!
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Fig. 12: Transformation or mapping in categorical language as a morphism (functor) between two categories; the problemcategory (Pro) and the solution-category (Sol). - "Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering"
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Buy a cheap copy of Abstract Algebra book by Pierre Antoine Grillet. The author has completely reworked this superb textbook for a fully updated new edition. He has reorganized many of the sections, and cut or shortened material... Free Shipping on all orders over $15.
Have you ever wondered how basic math operations like multiplication make life easier? Whether calculating the cost of multiple items or figuring out your total spending over several days, multiplication is everywhere. It saves us time and effort compared to manually calculating everything. With just a quick multiplication, we get our answers efficiently and in ... Read more
Biotensegrity is a conceptual model that is causing a paradigm shift in biomechanical thinking and changing the way that we think about functional anatomy.
JF Ptak Science Books Post 1252 This engraved plate from Abraham Rees' Cyclopedia... is the wonderful invention of Alexandre Choron (1771-1834), and appeared (perhaps for the first time in an English press) in London in 1814. It is a concise...
Mathematical Thinking D Angelo Solutions Manual. GitHub Gist: instantly share code, notes, and snippets.
Introduction to Mathematical Cognition - Camilla Gilmore, Silke M. Göbel, Matthew Inglis - ISBN: 9781138923959. The last decade has seen a rapid growth in our understanding of mathematical learning and performance and an increased recognition of the importance of the topic. The book traces the development of mathematical skills from basic number concepts to mathematical proofs, emphasising the hierarchical ...
Use your walls as a resource in your math classroom. Tips for setting up your room to make it functional for learning.
