I get so many emails that I may not reply, but I save all suggestions for puzzles/video topics.īook ratings are from January 2023.
#Altitude geometry problems software#
Be prepared-animation is time consuming and software can be expensive!įeel free to send me an email.
#Altitude geometry problems how to#
You can search for animation software tutorials on YouTube to learn how to make videos. Like many YouTubers I use popular software to prepare my videos. I studied Economics and Mathematics at Stanford University. It's been quite a journey! I thank everyone that has shared my work, and I am very grateful for coverage in the press, including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets. This does not affect the price you pay.)īy way of history, I started the Mind Your Decisions blog back in 2007 to share a bit of math, personal finance, personal thoughts, and game theory. As an Amazon Associate I earn from qualifying purchases. (As you might expect, the links for my books go to their listings on Amazon. I am also the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon. I run the MindYourDecisions channel on YouTube, which has over 1 million subscribers and 200 million views.
The correct answer is the textbook has a mistake because there is no triangle with the stated dimensions. Therefore, a right triangle with a hypotenuse of 10 can have an altitude on its hypotenuse of at most 5. This is largest when the third point is at the top or bottom of the circle, and the vertical distance is equal to the radius of the circle (half the length of the hypotenuse, which is the diameter of the circle). The vertical distance from the third point to the hypotenuse is the altitude to the hypotenuse. The hypotenuse must be the diameter of a circle, and the third point can be any point on the circle (except the endpoints of the hypotenuse). This means the two sides of the triangle must subtend a 180 degree angle in a circle. The angle opposite the hypotenuse must be a right angle of 90 degrees. Where can a third point be drawn to form a right triangle? The endpoints are two of the vertices for the triangle. A right triangle with a hypotenuse of 10 can have an altitude on its hypotenuse of at most 5, so its maximal area would be 25. The correct answer is there is no right triangle with the given dimensions. If the hypotenuse is taken as the base, and its altitude is taken as the height, then the area of the triangle would be (10)(6)/2 = 30. The area of a triangle is given by the formula (base)(height)/2. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. "All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. The story goes students quickly produced a calculation to this problem, but the teacher remarked that everyone was wrong. (rated 4.2/5 stars on 29 reviews) Kindle UnlimitedĪ geometry textbook has the following problem: “A right triangle has a hypotenuse equal to 10 and an altitude to its hypotenuse equal to 6. Math Puzzles Volume 3 is the third in the series. Math Puzzles Volume 2 is a sequel book with more great problems. Volume 1 is rated 4.4/5 stars on 112 reviews. Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory. Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers.
The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.3/5 stars on 116 reviews) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.3/5 stars on 290 reviews)Ĥ0 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. The Joy of Game Theory shows how you can use math to out-think your competition. (3) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias (2) 40 Paradoxes in Logic, Probability, and Game Theory (1) The Joy of Game Theory: An Introduction to Strategic Thinking Mind Your Decisions is a compilation of 5 books: If you purchase through these links, I may be compensated for purchases made on Amazon.
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