For those kids that like math and wish to boost their skills while having fun solving puzzles, here's a good site. It covers math from 1st grade through 6th grade as well as algebra.
http://www.mathsisfun.com/puzzles/
The specific category of puzzles are
starter, measuring, logic, shape, number, algebra, assorted math puzzles and quizzes, card, tricky, Einstein, Sam Loyd, symmetry jigsaw, puzzle games
Give them a shot and have fun!
Saturday, August 24, 2013
Tuesday, August 20, 2013
Sunday, August 18, 2013
Enjoy some of these math quotes and jokes!
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
"A mathematician is a device for turning coffee into theorems" (P. Erdos)
Addendum: American coffee is good for lemmas.
An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.
Old mathematicians never die; they just lose some of their functions.
Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. -- Goethe
Mathematics is the art of giving the same name to different things. -- J. H. Poincare
What is a rigorous definition of rigor?
There is no logical foundation of mathematics, and Gödel has proved it!
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
"A mathematician is a device for turning coffee into theorems" (P. Erdos)
Addendum: American coffee is good for lemmas.
An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.
Old mathematicians never die; they just lose some of their functions.
Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. -- Goethe
Mathematics is the art of giving the same name to different things. -- J. H. Poincare
What is a rigorous definition of rigor?
There is no logical foundation of mathematics, and Gödel has proved it!
Wednesday, August 14, 2013
the equation for a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1 if the transverse axis is horizontal and (y-k)^2/a^2 - (x-h)^2/b^2 = 1 if the transverse axis is the vertical axis.
The transverse axis it eht line segment connecting the vertices. The foci are located c units from the center, where c^2 = a^2 + b^2. The center, vertices and foci all lie along the transverse axis. The hyperbola opens along the transverse axis as well.
The transverse axis it eht line segment connecting the vertices. The foci are located c units from the center, where c^2 = a^2 + b^2. The center, vertices and foci all lie along the transverse axis. The hyperbola opens along the transverse axis as well.
Friday, August 9, 2013
Tips for graphing an ellipse.
The equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1 for an ellipse that is elongated along the x-axis.
The longer axis of the ellipse is the major axis and is of length 2a. The shorter axis of the ellipse is the minor axis and is of length 2b.
Plot the coordinate of the center (h,k) and move "a" units in each direction from the center along the major axis. Move "b" units from the center in each direction along the minor axis. These 4 points are the vertices. Then draw a smooth curve through the 4 points.
If you want to plot the foci, you need a value for c, which is found by c^2 = a^2 - b^2. Move c units from the center along the major axis in both directions and plot the point.
The equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1 for an ellipse that is elongated along the x-axis.
The longer axis of the ellipse is the major axis and is of length 2a. The shorter axis of the ellipse is the minor axis and is of length 2b.
Plot the coordinate of the center (h,k) and move "a" units in each direction from the center along the major axis. Move "b" units from the center in each direction along the minor axis. These 4 points are the vertices. Then draw a smooth curve through the 4 points.
If you want to plot the foci, you need a value for c, which is found by c^2 = a^2 - b^2. Move c units from the center along the major axis in both directions and plot the point.
Monday, August 5, 2013
When graphing a parabola from an equation in standard form, use these steps:
1. plot the vertez
2. plot the focus
3. draw the directrix line
4. find the latus rectum
5. draw the parabola
For example, graph the parabola with the equation (x - 2)^2 = 12(y + 1)
The form of a parabola that opens up or down is in the form (x - h)^2 = 4p(y -k), the vertex is (h,k), the focus is p units from the vertex in the direction the parabola opens, the directix is the line p units from the vertex in the opposite direction. The latus rectum is 4p. Plot a point 2p from the focus in both directions to determine the width of the parabola.
1. the vertex is (2, -1)
2. the focus is 3 units from the vertex.. Since p is positive the parabola opens up and the focus is at (2, 2)
3. the directrix is the horizontal line y = -1
4. the latus rectum is 12, so move 6 units to the left and right of the focus and plots those points.. The points are (8,2) and (-4,2)
5. now draw the parabola
1. plot the vertez
2. plot the focus
3. draw the directrix line
4. find the latus rectum
5. draw the parabola
For example, graph the parabola with the equation (x - 2)^2 = 12(y + 1)
The form of a parabola that opens up or down is in the form (x - h)^2 = 4p(y -k), the vertex is (h,k), the focus is p units from the vertex in the direction the parabola opens, the directix is the line p units from the vertex in the opposite direction. The latus rectum is 4p. Plot a point 2p from the focus in both directions to determine the width of the parabola.
1. the vertex is (2, -1)
2. the focus is 3 units from the vertex.. Since p is positive the parabola opens up and the focus is at (2, 2)
3. the directrix is the horizontal line y = -1
4. the latus rectum is 12, so move 6 units to the left and right of the focus and plots those points.. The points are (8,2) and (-4,2)
5. now draw the parabola
Thursday, August 1, 2013
How are the conic sections formed? Use paper and tape to create a double-napped cone. Then, using scissors, you can but the cone in 4 different ways.
1. A cut that is parallel to the base of the cone. The cross section on the surface of the cone is a circle.
2. A cute that is parallel to one of the sides of the cone. The cut will be through the other side of the cone and the base. This cross-section is a parabola.
3. A cut through both sides of the cone that is not parallel to the base. The cross-section is an ellipse.
4. A cut vertical through both cones. The cross-section is a hyperbola.
1. A cut that is parallel to the base of the cone. The cross section on the surface of the cone is a circle.
2. A cute that is parallel to one of the sides of the cone. The cut will be through the other side of the cone and the base. This cross-section is a parabola.
3. A cut through both sides of the cone that is not parallel to the base. The cross-section is an ellipse.
4. A cut vertical through both cones. The cross-section is a hyperbola.
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