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What did Hypatia contribute to math?

Hypatia was one of the first young women in her time to teach and study philosophy, mathematics and astronomy. She was regarded to be an astronomer and mathematician in her own right, writing commentaries and teaching students from her home. Her public lectures were very popular and attracted huge crowds.\nHypatia's intellect was nurtured by some of the best minds in the land, which enabled her to steer towards independence. Over time, she became a public speaker and often followed her father’s library faculty. Hypatia did work on conic sections and algebraic equations. Even though she ..

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What are some ways to teach students place value?

Laminate a set of place value cards with the digits zero through nine for each student, and then call out numbers, such as 43, 892, 3,526 or 23,467. Instruct students to use their cards to create the numbers on their desks, and distribute uncooked macaroni to represent commas. Place value cards are also helpful when students are learning to identify numbers in expanded form.\nPlace value people is a similar concept, except students are labeled with the digits zero through nine and use themselves to create given numbers. This activity works well with small groups, but it is also effective as an..

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What is a math trend?

As a conceptual example, if two sets of numbers are plotted and one set of values called x increases when the other set of values called y increases, there is a positive trend. More specifically, a model with mathematical equations needs to be defined by a curve fit. The least squares method finds the curve with the minimum deviation from all data points. Consider a set of data points (x1, y1), (x2, y2), ..., (xn, yn) where x is the independent variable, and y is the dependent variable. The fitting curve f(x) has deviation errors d1 = y1 - f(x1), d2 = y2 - f(x2), ..., dn = yn - f(xn). The best..

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What are polynomial operations?

Adding polynomials is a matter of combining like terms. If a polynomial includes the terms 3x and 4x they are like terms and add together to form 7x. Similarly, 2xy and 3xy add to form 5xy. However, it is not possible to combine the terms 4x and 2xy as they are not like terms. To subtract one polynomial from a second the signs of each term of the subtracted polynomial are changed and the two polynomials are added.\nTo multiply polynomials, multiply every term in the first polynomial by every term in the second polynomial. Once the multiplication process is completed, it is necessary to combine..

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What are some numbers that are divisible by four?

A quick way to tell if a large number is divisible by four is to look at the last two digits of the number. If they together represent a number divisible by four, the whole number is a multiple of four. For example, 5,789,416 is divisible by four because the last two digits, 16, represent a number into which four divides evenly. Likewise, 908 is divisible by four because 08 is a multiple of four. All multiples of four are even numbers, though not all even numbers are multiples of four.

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How many sides does a rhombus have?

The area of a rhombus can be calculated similarly to the area of a square or rectangle. The length of one side is multiplied by the altitude to calculate the shape's area. The altitude is the distance of a perpendicular line from one of the sides to the its opposite side.

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What is the derivative of tan (x)?

The first step in determining the tangent of x is to write it in terms of sine and cosine. The quotient identities indicate this equals the sine of x divided by the cosine of x.\nThe derivative of the tangent of x therefore equals the derivative of the sine of x divided by the cosine of x. This is obtained using the quotient rule. It equals the sum of the cosine squared of x plus the sine squared of x divided by the cosine squared of x.\nThe Pythagorean identity of sine and cosine allows this to be expressed as one divided by the cosine squared of x. It is then simplified and written as the se..

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How do you find the area of a rhombus?

Divide the rhombus into trianglesDraw the fast diagonal to divide the rhombus into two equal triangles. Assign the triangles labels A and B. Draw the second diagonal that passes through the center of the first diagonal. Measure the rhombusStretch the divider, and measure the first diagonal. Transfer the divider to a ruler, and read the measurement. Record it on the piece of paper. This is the base of triangles A and B. Do the same to find the value of the second diagonal. Divide the value of the second diagonal by 2 to get the height of either triangle.Calculate the area of the rhombusUsing a ..

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How do you calculate the value of an underlined digit?

In a number, place values from right to left are ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions and so on. By definition, a place value number is a 1 followed by a number of zeros. An example calculation of the value of an underlined digit would be if the digit 4 were underlined in 1040, the underlined value of that digit would be 40.

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How many lines of symmetry does a triangle have?

For any triangle, a line of symmetry must bisect an angle and the side opposite that angle, dividing the triangle into two equal right triangles. For this to be true, the original triangle must have at least two equal sides. For an isosceles triangle, the line of symmetry bisects the obtuse angle and the side opposite it. For an equilateral triangle, since all sides and angles are equal, the lines of symmetry can bisect any of the angles. Since a scalene triangle has no equal sides or angles, it can have no lines of symmetry.

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