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19 December, 2024 in expository, math.MG | Tags: cosmic distance ladder, quaternions, spherical trigonometry | by Terence Tao | 11 comments Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and...
Chaos theory is closely linked to thebutterfly effect,the idea that a very slight variation in initial conditions can result in substantial changes in output values. This runs counter to the intuitive idea that similar initial conditions should result in roughly similar outputs. This concept frequent...
Crucially, Desmos also helps take students from a basic understanding of graphs into far more complex possibilities. In fact, there is an annual Desmos competition that has entrants create complex and often beautiful artwork outputs using math to build the images in graph form. What is D...
Similarly, if you give the AI an either-or choice, a few examples of how you want it to respond, or ask it to format its results in a certain way, you're likely to get better outputs with fewer hallucinations. Finally: expect hallucinations. No matter how careful you are, expect any...
What's in a Reproducible Example? Parts of a reproducible example: background information - Describe what you are trying to do. What have you already done? complete set up - include any library() calls and data to reproduce your issue. data for a reprex: Here's a discussion on set...
For instance, the following line of code reads a single character from the keyboard and outputs its ASCII code. int ch; printf("Enter a character: "); ch = getchar(); printf("The ASCII code of %c is %d\n", ch, ch); This program asks the user to enter a character, then reads...
in the PUBMED/Scopus database. Our search included several terms related to AI and urooncology. Articles were selected with the consensus of all authors. Results: Several types of AI can be used in the medical field. The most common forms of AI are machine learning (ML), deep learning (...
a function relates inputs to outputs a function takes elements from a set (the domain) and relates them to elements in a set (the codomain). all the outputs (the actual values related to) are together called the range a function is a special type of relation where: every element in ...
Both o1-preview and o1-mini are great for solving complex problems in math, coding, and science. Here’s an example of o1-preview in action: The o1-mini model is also useful for writing and debugging complex code. It’s faster and “80% cheaper than o1-preview,” according to OpenAI....