Podcast: DownloadEuclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem, and that in...
Options for Printing and Prepping the Puzzle
There are several options for printing and prepping this puzzle.
The easiest way to distribute this puzzle...
Subtraction of 3-digit numbers with regrouping are explained here with examples.As you borrow from the tens column, you can borrow from the
hundreds column also.REMEMBER:1...
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Google’s mistake with Gemini
You have probably heard that Google had to suspend it’s Gemini image feature after showing people...
HP Prime and Numworks: Plotting a Parametric Line of Motion
Plotting
the Position of Motion
This program draws a 2D motion plot from an initial starting point
(x,...
Quick math-personality quiz: What is seven-and-one-fourth minus three-fourths, expressed as a mixed number (a whole number plus a proper fraction)?
What matters isn’t what answer...
Joel David Hamkins and Theodor Nenu, “Did Turing prove the undecidability of the halting problem?”, 18 pages, 2024, Mathematics arXiv:2407.00680.
Abstract. We discuss the...
In 3rd grade, students transition from plotting, ordering, and comparing 3-digits numbers to performing the same skills with 4-digit numbers. This prepares them for...
Mathematics is a fascinating subject that influences various aspects of our lives, from architecture to technology. To ignite your students' passion for math and...
Are you a new geometry teacher searching for innovative resources to kickstart your classroom? Or perhaps you're an experienced educator seeking fresh ideas to...
I gave a talk for the Food for Thought seminar for the Notre Dame philosophy department.
The topic concerned definite descriptions, particularly the semantics...
Starters collection – KS3 to A LevelSee also Custom Maths Revision Starters
Functional SkillsIncluded in the Functional Skills collection are Maths Made Memorable, Dr Frost Learning, and Transum Mathematics, all of...
dedicated to Norman Skliar and Sidney Cahn
In an earlier blog-essay, When 1+1 Equals 0, I explained how 1 + 1 = 0 makes sense in mod 2 arithmetic; today...
A Little AIME Problem
Posted: May 16, 2022 in Mathematics Tags: AIME, math, Math Contest
Solution
In general, let
By Pythagoras Identity,
Solve this system by adding and subtracting, we get
Hence,
and
Therefore,
Let , then