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REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK HOW TO DO… R-SIN-ALPHA QUESTIONS That looks like a simultaneous equation to me. It’s a bit tricky because they’re non-linear, but don’t let a thing like that bother you: divide the R sin. . ( α) one by the R cos. . ( α) one and the R s cancel to leave you with tan. . ( α) = 5 3. You can throw that in your calculator and get an answer out - SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK HOW TO DO… R-SIN-ALPHA QUESTIONS That looks like a simultaneous equation to me. It’s a bit tricky because they’re non-linear, but don’t let a thing like that bother you: divide the R sin. . ( α) one by the R cos. . ( α) one and the R s cancel to leave you with tan. . ( α) = 5 3. You can throw that in your calculator and get an answer out - SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
ASK UNCLE COLIN: THE CONSTANT TERM This website does not use cookies. We do not store any personally identifiable information about visitors. Some pages contain affiliatelinks.
REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it RANDOM NUMBER TABLES 165 991 (reject) 183 450 (reject) 424 943 (reject) 082 377 328 783 (reject) 543 (reject) 334 899 (reject) 455 (reject) 687 (reject and start the next colum) 244 172 ( the next eight require rejecting ) 407. So, the selection for our sample is 165, 183, 424, 082, 377, 328, 334, 244, 172 and 407. Don’t try to tell me you’d rather have a SPHERICAL CAPS AND COORDINATE SYSTEMS Of the four problems, this one felt the least difficult to me. Splitting the segment into disks of height δ x and radius R 2 − x 2 gives a volume of π ∫ ( R 2 − x 2) d x, between limits of R cos. ( α)]. This fits: if cos. ( α) = 1, the integral vanishes; if it’s 0, we get the volume of a hemisphere, and if it’s THE MATHEMATICAL NINJA AND THE $N$TH TERM Note: this post is only about arithmetic and quadratic sequences for GCSE. Geometric and other series, you’re on your own. Quite how the Mathematical Ninja had set up his classroom so that a boulder would roll through it at precisely that moment, the student didn’t have time to ponder. He ran along in front of it, with the Indiana Jones theme playing in his head for a few seconds before ASK UNCLE COLIN: INCIRCLES Dear Uncle Colin, I noticed that the incircle of a 3-4-5 triangle has a radius of 1, and for a 5-12-13 triangle, it’s 2. Is it always an integer in a Pythagorean triangle? Having Elegant Radius Or Not? THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” DICTIONARY OF MATHEMATICAL EPONYMY: THE KOVALEVSKAYA TOP The Kovalevskaya top goes all over the shop!< /p>. When it’s not moving very fast, gravity is the important thing and the motion is a combination of the pendulum rotating in two possible directions, while the cross itself rotates around the pendulum. That’s neat in itself. When it’s moving fast, gravity isn’t the dominant force any more. THE DICTIONARY OF MATHEMATICAL EPONYMY: THE EULER BRICK The list of things named after Leonhard Euler on Wikipedia runs to about 1500 words, and, I would hazard, omits several such things.. So how to settle on one? I’ve come down on one of the greatest “low barrier, high ceiling” problems there is: it’s a conjecture so simple, you can grasp it as soon as you’ve got a sense of Pythagoras’s theorem, but so complicated that people have FINDING CONSTANTS FOR A LINE OR CURVE Finding constants for a line or curve - Secrets of the Mathematical Ninja. May 5, 2014. The Mathematical Ninja stopped dead in their tracks. Not literally, of course: immortal beings don’t die. They turned their head slowly towards the student, unsure what was going on. They probably had in mind their recent OFSTED report, which had– while
"HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that itREGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it FLYING COLOURS MATHS: MATHS TUTOR IN WEYMOUTH Writing. I'm the author of a several maths books, including the UK Maths For Dummies titles and a range of A-level e-books answering the big questions about the big topics.. I also write the Flying Colours Maths Blog, which gives all sorts of insights into the mathematical mind -- from the Secrets of the Mathematical Ninja to maths quotations.. Speaking of which - sign up for the Sum Comfort ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
"HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that itREGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it FLYING COLOURS MATHS: MATHS TUTOR IN WEYMOUTH Writing. I'm the author of a several maths books, including the UK Maths For Dummies titles and a range of A-level e-books answering the big questions about the big topics.. I also write the Flying Colours Maths Blog, which gives all sorts of insights into the mathematical mind -- from the Secrets of the Mathematical Ninja to maths quotations.. Speaking of which - sign up for the Sum Comfort ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
ABOUT | FLYING COLOURS MATHS Hi! My name is Colin, and I am a mathematician. I write books and articles to make maths as clear as possible for as many as possible.. Writing about maths wasn’t originally part of the plan. I was an academic for a while – I worked on NASA’s Living with a Star program at Montana State University, keeping the world safe from solar flares((I think I did a pretty good job of that ASK UNCLE COLIN: THE CONSTANT TERM This website does not use cookies. We do not store any personally identifiable information about visitors. Some pages contain affiliatelinks.
REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it THE DICTIONARY OF MATHEMATICAL EPONYMY: THE EULER BRICK The list of things named after Leonhard Euler on Wikipedia runs to about 1500 words, and, I would hazard, omits several such things.. So how to settle on one? I’ve come down on one of the greatest “low barrier, high ceiling” problems there is: it’s a conjecture so simple, you can grasp it as soon as you’ve got a sense of Pythagoras’s theorem, but so complicated that people have POWERS | FLYING COLOURS MATHS “Here’s a quick one,” suggested a fellow tutor. “Prove that $2^{50} < 3^{33}$.” Easy, I thought: but I knew better than to sayit aloud.
SPHERICAL CAPS AND COORDINATE SYSTEMS Of the four problems, this one felt the least difficult to me. Splitting the segment into disks of height δ x and radius R 2 − x 2 gives a volume of π ∫ ( R 2 − x 2) d x, between limits of R cos. ( α)]. This fits: if cos. ( α) = 1, the integral vanishes; if it’s 0, we get the volume of a hemisphere, and if it’s A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATING A Puzzle From The MathsJam Shout (With Generating Functions) In a recent MathsJam Shout, courtesy of Bristol MathsJam, we were given a situation, which I paraphrase: Cards bearing the letters A to E are shuffled and placed face-down on the table. You predict which of the cards bears which letter. (You make all of your guesses beforeanything is
FLYING COLOURS MATHS: MATHS TUTOR IN WEYMOUTH Writing. I'm the author of a several maths books, including the UK Maths For Dummies titles and a range of A-level e-books answering the big questions about the big topics.. I also write the Flying Colours Maths Blog, which gives all sorts of insights into the mathematical mind -- from the Secrets of the Mathematical Ninja to maths quotations.. Speaking of which - sign up for the Sum Comfort THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
"HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that it A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
"HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that it A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
ASK UNCLE COLIN: THE CONSTANT TERM This website does not use cookies. We do not store any personally identifiable information about visitors. Some pages contain affiliatelinks.
THE DICTIONARY OF MATHEMATICAL EPONYMY: THE EULER BRICK The list of things named after Leonhard Euler on Wikipedia runs to about 1500 words, and, I would hazard, omits several such things.. So how to settle on one? I’ve come down on one of the greatest “low barrier, high ceiling” problems there is: it’s a conjecture so simple, you can grasp it as soon as you’ve got a sense of Pythagoras’s theorem, but so complicated that people have RANDOM NUMBER TABLES 165 991 (reject) 183 450 (reject) 424 943 (reject) 082 377 328 783 (reject) 543 (reject) 334 899 (reject) 455 (reject) 687 (reject and start the next colum) 244 172 ( the next eight require rejecting ) 407. So, the selection for our sample is 165, 183, 424, 082, 377, 328, 334, 244, 172 and 407. Don’t try to tell me you’d rather have a SPHERICAL CAPS AND COORDINATE SYSTEMS Of the four problems, this one felt the least difficult to me. Splitting the segment into disks of height δ x and radius R 2 − x 2 gives a volume of π ∫ ( R 2 − x 2) d x, between limits of R cos. ( α)]. This fits: if cos. ( α) = 1, the integral vanishes; if it’s 0, we get the volume of a hemisphere, and if it’s THE ‘DATING RULE’ Two things: the somewhat random-looking picture above is from The Moon Is Blue, a 1953 film that’s the first known reference to the ‘dating rule’ discussed here. Secondly, I don’t make any judgement about the validity of the ‘dating rule’ - you might find it a useful rule of thumb or a ludicrous restriction; I find it a nice thing to do some algebra on. WHAT’S THE PLOT, EPISODE 2 For the record, the actual function I plotted was $\left( x^2 + \frac{x}{y} - 3\right)^2 \le 8$. Stay tuned for the next unmissable episode of What’s The Plot, probably in a few weeks’ time! CAPTAIN HOLT’S SEESAW Captain Holt's Seesaw. Jul 13, 2020. When Jake’s father (Bradley Whitford) comes to town, Jake is excited to see him, but Charles is wary of his intentions; Holt challenges Amy, Terry, Gina and Rosa with a brain teaser in exchange for Beyonce tickets. Brooklyn 99, S02 E18,Captain Peralta.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” ASK UNCLE COLIN: INCIRCLES Dear Uncle Colin, I noticed that the incircle of a 3-4-5 triangle has a radius of 1, and for a 5-12-13 triangle, it’s 2. Is it always an integer in a Pythagorean triangle? Having Elegant Radius Or Not?REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it "HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that it A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
"HOW DO I KNOW WHICH METHOD TO USE If there’s an ugly bracket or bottom of a fraction, try the substitution u = the ugly thing. If there’s a ln. . ( x) or similar knocking around, it almost certainly by parts - let u be the logarithm. If there’s an x n multiplied by a function, try parts - let u be x n and hope that it A PUZZLE FROM THE MATHSJAM SHOUT (WITH GENERATINGSEE MORE ON FLYINGCOLOURSMATHS.CO.UK ASK UNCLE COLIN: INVARIANT LINES So the two equations of invariant lines are y = − 4 5 x and y = x. Just to check: if we multiply M by ( 5, − 4), we get ( 35, − 28), which is also on the line y = − 4 5 x. Similarly, if we apply the matrix to ( 1, 1), we get ( − 2, − 2) – again, it lies on the given line. (It turns out that these invariant lines are related in SPHERICAL CAPS AND COORDINATE SYSTEMS BASIC MATHS SKILLS: THE ICE CREAM PORTION As you might know (if you’ve spotted the big yellow bar above), I’m training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer’s Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn’t be good for me if I wasn’t pounding out 40-odd miles a week. A STUDENT ASKS: WHY DO YOU LOVE MATHS SO MUCH? It’s a really hard question to answer - if you asked someone why they like music or football, they’d probably shrug and say ‘I just do!’. There are loads of things I love about maths - on one hand, it’s this brilliant, creative game that’s completely limitless and at the same time very strict about what you can do; and on the other WHY IS $\ARCOSH$ THE POSITIVE ROOT? Waving a hand at it. Three heuristic reasons that you need the positive root: Obviously the bigger root is the positive one, so - given that cosh. . ( x) is symmetrical about the y -axis, we need the positive root. The roots z 1 and z 2 of the quadratic equation (*) have a product of 1 - so z 1 = 1 z 2 and y 1 = − y 2 using the logrules.
ASK UNCLE COLIN: LAYING BRICKS Thinking it through (1) For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks. But we want 3150 bricks. That will take the two builders longer - by a factor of 31502800 = 9 8.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” HOW TO DO A TRIGONOMETRY PROOF: FIVE TOP TIPS First up, a horrible confession: I like teaching the higher-lever core maths modules (C3 and C4), because they’re closer to ‘real’ maths than the AS-level ones. One of the things that sets them apart is the introduction of proofs, usually for trigonometry ((There’s sometimes a wee bit of proof in C1 and C2, but C3 is where it reallykicks off.)).
ASK UNCLE COLIN: THE CONSTANT TERM This website does not use cookies. We do not store any personally identifiable information about visitors. Some pages contain affiliatelinks.
THE DICTIONARY OF MATHEMATICAL EPONYMY: THE EULER BRICK The list of things named after Leonhard Euler on Wikipedia runs to about 1500 words, and, I would hazard, omits several such things.. So how to settle on one? I’ve come down on one of the greatest “low barrier, high ceiling” problems there is: it’s a conjecture so simple, you can grasp it as soon as you’ve got a sense of Pythagoras’s theorem, but so complicated that people have RANDOM NUMBER TABLES 165 991 (reject) 183 450 (reject) 424 943 (reject) 082 377 328 783 (reject) 543 (reject) 334 899 (reject) 455 (reject) 687 (reject and start the next colum) 244 172 ( the next eight require rejecting ) 407. So, the selection for our sample is 165, 183, 424, 082, 377, 328, 334, 244, 172 and 407. Don’t try to tell me you’d rather have a SPHERICAL CAPS AND COORDINATE SYSTEMS Of the four problems, this one felt the least difficult to me. Splitting the segment into disks of height δ x and radius R 2 − x 2 gives a volume of π ∫ ( R 2 − x 2) d x, between limits of R cos. ( α)]. This fits: if cos. ( α) = 1, the integral vanishes; if it’s 0, we get the volume of a hemisphere, and if it’s THE ‘DATING RULE’ Two things: the somewhat random-looking picture above is from The Moon Is Blue, a 1953 film that’s the first known reference to the ‘dating rule’ discussed here. Secondly, I don’t make any judgement about the validity of the ‘dating rule’ - you might find it a useful rule of thumb or a ludicrous restriction; I find it a nice thing to do some algebra on. WHAT’S THE PLOT, EPISODE 2 For the record, the actual function I plotted was $\left( x^2 + \frac{x}{y} - 3\right)^2 \le 8$. Stay tuned for the next unmissable episode of What’s The Plot, probably in a few weeks’ time! CAPTAIN HOLT’S SEESAW Captain Holt's Seesaw. Jul 13, 2020. When Jake’s father (Bradley Whitford) comes to town, Jake is excited to see him, but Charles is wary of his intentions; Holt challenges Amy, Terry, Gina and Rosa with a brain teaser in exchange for Beyonce tickets. Brooklyn 99, S02 E18,Captain Peralta.
THE NAMES OF THE ISLE OF PORTLAND Portland, Oregon, is one of the places in the USA that takes great pride in its self-conscious kookiness – you see bumper stickers saying ‘Keep Portland Weird’, just like you do in Asheville, North Carolina and Austin, Texas, and probably another dozen cities who, if they were people, would go around saying “I’m mad, me!” ASK UNCLE COLIN: INCIRCLES Dear Uncle Colin, I noticed that the incircle of a 3-4-5 triangle has a radius of 1, and for a 5-12-13 triangle, it’s 2. Is it always an integer in a Pythagorean triangle? Having Elegant Radius Or Not?REGIONS OF A CIRCLE
The first line, to the neighbour, crosses no lines, and adds one region. The second line, to point 2, splits the circle so there is one point to the left and three to the right, all of which are connected - so this line adds 1 × 3 + 1 regions. The third line splits the circle two on each side, so it Mathematical headaches? Problem solved! Hi, I'm Colin, and I'm here to help you make sense of maths* Home
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TEACHING
To book a class, just call 07796 430 862 ! Maybe you're studying for your A-levels, or struggling with a university course, or going back to school to earn a numeracy qualification. Whatever level you're working at, I'm here to help you succeed with calm, supportive and friendly maths classes. I've been a full-time maths tutor since 2008 and helped hundreds of students get over their fears and get to grips with maths. TO ARRANGE CLASSES OR FIND OUT MORE ABOUT LEARNING WITH FLYING COLOURS MATHS, PLEASE CLICK HERE .Read More...
WRITING
I'm the author of a several maths books, including the UK Maths ForDummies
titles and a range of A-level e-booksanswering
the big questions about the big topics. I also write the Flying Colours Maths Blog , which gives all sorts of insights into the mathematical mind -- from the Secrets of the Mathematical Ninja to maths quotations. SPEAKING OF WHICH - SIGN UP FOR THE SUM COMFORT EMAIL NEWSLETTER ON THE RIGHT AND GET A FREE E-BOOK OF MY 20 FAVOURITE MATHEMATICALQUOTES.
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SERVICES
Whether you need a detailed solution to a mathematical problem, a custom Excel spreadsheet to solve a persistent issue, or need some technical maths translated into plainer English, I offer a wide and flexible range of consulting services to make your maths headachesvanish - fast.
IF YOU NEED A MATHS MIRACLE, CALL ME ON 07796 430 862.Read More....
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* Regions of a circle * Wrong, But Useful: Episode 70 * Ask Uncle Colin: Why is e not 1? * Dictionary of Mathematical Eponymy: Hoberman Sphere * Ask Uncle Colin: Curved Surface Areas FROM THE ARCHIVES… Wrong, But Useful: Episode 47August 22, 2017
In this month's episode of Wrong, But Useful, we are joined by Special Guest Co-Host @jussumchick, who is Jo Sibley in real life. Colin's audio is unusually hissy in this one, which is why it’s a little late; he apologises for both inconveniences. We discuss: Read more…MATHEMATICAL QUOTES
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QUOTABLE MATHS: TAO
ABOUT COLIN BEVERIDGE, MATHS TUTOR IN WEYMOUTH, DORSETColin Beveridge
Maths tutor and author in Weymouth, Dorset and online > THERE'S NOTHING QUITE LIKE A 'LIGHTBULB MOMENT' WHEN A STUDENT > SUDDENLY SAYS "OH! THAT'S EASY!" AND WE BOTH KNOW THEY UNDERSTAND.INTRODUCTION
Hi! I'm Colin.
I've been a maths tutor on and off since I was in high school - originally for family and friends, then more formally at university and as a researcher. When I left academia in 2008, it was an obvious way to make ends meet while I looked for a 'proper job' - but I soon found that teaching maths was far more enjoyable than real work. MY APPROACH TO MATHS TUTORING If you want to learn maths, I'll help you. It's fine to forget stuff, it's fine to ask questions - even if you forget how to count, I'll still help you. As long as you put the workin, you'll do well.
One of the benefits of one-to-one maths tutoring is that I can take the time to find the root cause of an issue and help to put it right - and sometimes that means going back to the basics. There's no shame in that - if something needs fixing, we should fix it. These days, I teach mainly: * University-level maths, and maths for scientists * A-level maths, and the mathematical parts of other subjects * Adult numeracy and QTS test preparation I'm afraid I have very limited availability for GCSE students, and unfortunately I can't currently take on students below Year 11. One-to-one lessons at my classroom in Weymouth start at £45 per hour. I also offer individual maths classes over Skype using an onlinewhiteboard.
To book a lesson, please call me on 07796 430 862 or email colin@flyingcoloursmaths.co.uk with your details, and I'll get back to you as soon as I can. MATHEMATICAL WRITING My first published book, Basic Maths For Dummies,
came out in August 2011, and is in bookstores across the country and online. I'm also the author of several other maths books in the For Dummies series and a number of e-books aimed at simplifying A-level maths. To learn more about my maths books, click here .MATHS SERVICES
When your kitchen floods, you call a plumber. When your Large Hadron Collider breaks, you call a quantum mechanic. And when you have a mathematical crisis, you call me on 07796 430 862.
If it's something I can help with, I'll move heaven and earth to get it put right. If it's something I cannot help with, chances are that I can put you in touch with someone who can.MEDIA AND SCHOOLS
I'm delighted to talk to media outlets from school newspapers to worldwide conglomerates about any aspect of maths. Give me a call on 07796 430 862 and we'll figure something out. If you'd like me to write you an article, just email me on colin@flyingcoloursmaths.co.uk. And if you'd like me to give a talk, that can also be arranged (depending on my schedule).MATHS BACKGROUND
I studied Maths with French at the University of St Andrews (I graduated with a 2:1 in 2000) and went on to do a PhD there, which I finished in 2003. I then spent four years as a physics researcher at Montana State University - I studied the structure of magnetic fields around the Sun and how they might store energy for release in solar flares. My main contribution to science was a simple equation that about six people worldwide will ever have a use for, but I can at least say I have an equation named after me.
That was one of the reasons I left - what I was doing wasn't really helping anyone apart from me and my boss. As a maths tutor, I feel like I'm making a genuine, positive difference to students' lives. There's nothing quite like a 'lightbulb moment' when a student suddenly says "Oh! That's easy!" and we both know they understand. Baby Bill, taking after his dad. It's also nice to be my own boss.OUTSIDE OF MATHS
When I'm not teaching, I'm mainly looking after Baby Bill. In what little free time I have left, I play some music - I'm a keen singer/songwriter and am currently trying to learn to play the mandolin. I'm also a reluctant runner (I completed the Berlin Marathon in 2013... never again!), and I mess about on the computer when I getthe chance.
WHERE DO YOU TEACH?
I teach in my home in Abbotsbury Road, Weymouth. It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.Map Data
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If this isn't true, it bloody well should be. twitter.com/bobby_seagull/stat… August 9, 2019 9:01 am*
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