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Mathematicians

Often, to completely understand the importance of a mathematical theory, it's essential to know about the person who developed it. This category is where all questions about historically significant mathematicians should be asked.

6,570 Questions

Is Chebyshev linkage an inversion of four bar linkage?

Well, yes: but that isn't very interesting. The Chebyshev linkage does have four bars, and by definition, every four bar linkage has four inversions.

An 'inversion' of a linkage just means you're holding a specific bar still, or in kinematic terms, you're using that link as the 'ground link'. If a linkage has arms A, B, C, and D, the first inversion uses A as the ground link, the second inversion uses B as the ground link, the third inversion uses C as the ground link, and the fourth inversion uses D as the ground link.

Inversions matter because of the 'coupler' link, which is the one opposite the ground link. Take the first inversion of A, B, C, D above: A is the ground link, so it doesn't move relative to the ground. B and D connect to A, so both of them have one end that doesn't move relative to the ground. The other ends of B and D move in circular arcs relative to the ground (they're lines of constant length, with one end fixed relative to the ground.. in other words, a compass). Link C is the coupler for this inversion, because it's connected to the moving ends of both B and D. It moves in and interesting way relative to the ground.

For each inversion, a different link is the coupler, and the motion of the coupler relative to the ground tends to be VERY different from one inversion to the next. The motion of any given point on the coupler relative to ground is a sixth-order curve (meaning it start with x to the 6th power and works down from there), and people are still doing hard work on the math.

The Chebyshev linkage is interesting because the center of the coupler moves in almost exactly a straight line. It wobbles a little, but the wobble is small enough that they could ignore it when making parts for steam engines that needed to move in a straight line.

An interesting side effect of coupler curves being sixth-order functions is that there are three completely different linkages whose couplers will move the same way. Chebyshev was one of the people who did the math to prove that. The three linkages whose couplers move the same way are called 'cognates' of each other.

The Chebyshev linkage is symmetric, so both of its cognates look the same. They're called the 'Hoekens' linkage, after the guy who did that bit of math.

What did Rene descartes emphasize and assert?

"Descartes emphasized the importance of his own mind. He asserted that he would accept only those things that his reason were true."

- GLENCOE WORLD HISTORY

What did the nativists of the 1920s believe in?

Nativists believed there was a need to protect citizens against new immigrants. They believed the foreign born were inferior to native born United States citizens, and that they threatened the American way of life, as well as took away jobs that should go to American citizens.

What experience do you have in this field?

I have experience in various areas within this field, including research, analysis, writing, and project management. I have worked on a range of projects and collaborated with teams to achieve successful outcomes. My expertise includes data analysis, report writing, and strategic planning.

What is negative 15-7?

Fact: when their is two negative you add meaning if you have -3-5 yo add 3 and 5 then put back the negative sign. therefore (-15-7) = -22

How do you make working model of Pythagoras theorem in grade 9?

Construct a right angle triangle with a base of 3 units, a height of 4 units with a hypotenuse of 5 units and then:-

Enlarge the base to 3 by 3 square units = 9 squares

Enlarge the height to 4 by 4 square units = 16 squares

Enlarge the hypotenuse to 5 by 5 square units = 25 squares

Thus proving Pythagoras' theorem: a2+b2 = c2 whereas a and b are the sides of the triangle with c being its hypotenuse or longest side

Who was maria gaetana agnesi's husband?

Maria Agnesi didn't actually have a husband or children.

She devoted her whole life studying equations and helping poor women.

When did René Descartes invent the coordinates?

Descartes was a very philosophical person. In fact he's the father of modern philosophy

He thought the world on 3 axes, he had to do this while he was trying to solve the riddle of pappus.

But to be more specific he invented the coordinate system while he was sleeping with one oven at he's side and had 3 dreams.

the answer you're looking for, is that "Descartes dreamt the coordinate system, then he did it reality on a compendium of one of he's 3 books of philosopy"

Who invented the formula for circular motion?

Sir Zvince Catervuent. A French scientist, he never really liked his job!