Browsing category geometry

Ask Uncle Colin: Find me a circle!

Dear Uncle Colin, I have two points and I want to construct a circle of a given radius that passes through them. Is it possible? -- Every Underspecified Circle Lives Its Dream Hi, EUCLID, and thanks for your message! There are three possible answers to this, depending on the size

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Ask Uncle Colin: Can you prove $\sin(2x) \equiv 2\sin(x)\cos(x)$?

Dear Uncle Colin, I find it easier to remember trigonometric identities if I can 'see' how they fit together. I'm expected to know that $\sin(2x) \equiv 2\sin(x)\cos(x)$, but haven't been able to prove it. Any ideas? -- Geometry? Right Angles? How About Medians? Hi, GRAHAM! My favourite proof jumps out

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A MathsJam Masterclass: A Circle That Won’t Behave

Somewhere deep in the recesses of my email folder lurks a puzzle that looks simple enough, but that several of my so-inclined friends haven't found easy: A circle of radius $r$, has centre $C\ (0,r)$. A tangent to the circle touches the axes at $A\ (9,0)$ and $B\ (0, 2r+3)$.

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Ask Uncle Colin: A pentagonal rhombus

Dear Uncle Colin, I've carelessly interlocked a couple of regular pentagons together like this and need to find the area of the overlap because of reasons. For still other reasons, I don't want to use trigonometry. How do I negotiate my way through this minefield? Trigonometry's Always Overrated Hi, TAO,

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Ask Uncle Colin: how do you find the intersection of three circles?

Dear Uncle Colin, I've been challenged to find the area of the intersection of three circles while drawing a Venn diagram. I don't know where to start!-- Triangle Unpredictably Rounded; I'm No Genius For a moment, TURING, I thought there wasn't a problem in this problem, but then I realised:

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How the Mathematical Ninja explains the Mathematical Pirate’s circle trick

"Let me see that!" commanded the Mathematical Ninja, looking at one of the Mathematical Pirate's blog posts. "That's... but that's..." "It's not wrong!" said the Mathematical Pirate, smugly. "It just works!" "But you're presenting it as magic, not as maths." The Mathematical Pirate nodded eagerly. "Lovely magic! How does it

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How the Mathematical Pirate finds the centre and radius of a circle

"Arr?" said the student, really not sure. "No, no, $r$," said the Mathematical Pirate. "The centre is at C -- or $(a,\, b)$, if you prefer -- and the radius is $r$." "Gotcha. So, if you've got something like $x^2 + y^2 + 8x - 12y + 3=0$, how do

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A circle problem that succumbs to a circle theorem

A tweet from @GregSchwanbeck some time back asked: Does square or circle have greater perimeter? A surprisingly hard prob for HS: http://t.co/vwLIs26pcC #mathchat #math pic.twitter.com/Vpjop8yU7G — Greg Schwanbeck (@GregSchwanbeck) March 16, 2015 The setup is: one side of a square is tangent to a circle, and two corners of the

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Minecraft circles

I have a confession to make. One that will lower me seriously in the esteem of my 10-year-old nephew: I don't really get Minecraft. Sorry, buddy. I've tried it. I love that you love it -- honestly, creative games are awesome for your problem-solving skills and breaking down the barriers

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Normals to an ellipse: a Core 4 masterclass

A reader (not, in fact, a Core 4 student) wrote in to ask: I have an ellipse in my spreadsheet program, using the formula $y = \frac ba \sqrt{a^2 - x^2}$, and I want to know the angle the normal to the ellipse makes with the horizontal at any value

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