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Tuesday, November 25

  1. page Project Euler edited Peter Nugent Project Euler Problem 15- Starting in the top left corner of a 2×2 grid, and only be…
    Peter Nugent Project Euler
    Problem 15- Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner. How many such routes are there through a 20×20 grid? (96463 solved)
    To solve this problem, I represented the paths as a series of R’s and D’s, representing right and down steps. For a K×K grid, the path must be 2K long, containing K R’s and K D’s. You can solve this using a choose function to find all the valid combinations of R’s and D’s. For a 20×20 grid, it will be a 40 step path with 20 R’s and 20 D’s, so we can find them all by performing the function 40 choose 20. This gives a number that would be impractical to calculate by hand, so I used Wolfram Alpha to find the solution.
    Solution- 137846528820
    Problem 16- 215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 21000? (120664 solved)
    This problem is fairly straightforward, but the value 21000 is far too large to do by hand or even a regular calculator. To solve this, I used Wolfram Alpha to find 21000. Afterwards, I also used Wolfram Alpha to find the sum of its digits, even though it would have been possible to do by hand or with a less powerful calculator.
    Solution- 1366
    Problem 18- If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used? (79465 solved)
    To solve this problem, I had to use some code someone else had already written. I found it on a Microsoft support site discussing changing numbers from numerals to words on Excel. I found the code I needed here - http://support.microsoft.com/kb/213360. I used this for the numbers 1-1000. After that, I used the character count function in Excel, and subtracted the amount of spaces in each number, as they are not counted in our solution, but are counted by the character counter. Finally, I used a sum on the cells with the character counters to arrive at our final solution. Without excel, this would have been doable, but much more time consuming and with much more room for error.
    Solution- 21124

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    9:33 am

Monday, November 17

  1. page home edited ... Riemann Sums and Discussion Geogebra Constructions Tech Activity Here is a picture of Lil…
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    Riemann Sums and Discussion
    Geogebra Constructions
    Tech Activity
    Here is a picture of Lilly by a river on a very cold morning
    {Lilly.jpg}
    (view changes)
    10:54 pm

Tuesday, October 21

  1. page Spreadsheet with Excel edited {451ExcelProject.xlsx} Note- the lattice multiplication spreadsheet is having troubles with the…
    {451ExcelProject.xlsx}
    Note- the lattice multiplication spreadsheet is having troubles with the feedback. I will visit you during office hours this week to try and figure out what I am doing wrong.
    Discussion Question-
    1. Using Google documents can have many advantages. The first being that you can access it with just a browser, rather than having to install excel. Another is that it is so easy to have multiple people working on it at the same time, where Excel cannot be edited by multiple people simultaneously.
    2. Excel can be useful for things as well. A large part is that many companies already use it, so understanding how to use it could give you a jump start when you start working there. Another reason it could be better is it does not require internet access. Once the software is installed, you can use excel anywhere you could bring your laptop.

    (view changes)
    9:43 am

Tuesday, October 14

  1. page home edited ... I have a bonsai tree \sin^2(\theta)+\cos^2(\theta)=1 Spreadsheets Google Doc Crossed Ladd…
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    I have a bonsai tree
    \sin^2(\theta)+\cos^2(\theta)=1
    Spreadsheets Google Doc
    Crossed Ladders Problem
    Riemann Sums and Discussion
    (view changes)
    9:35 am

Tuesday, October 7

  1. page home edited ... Crossed Ladders Problem Riemann Sums and Discussion Geogebra Constructions Here is a pict…
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    Crossed Ladders Problem
    Riemann Sums and Discussion
    Geogebra Constructions
    Here is a picture of Lilly by a river on a very cold morning
    {Lilly.jpg}
    (view changes)
    9:55 am
  2. page Dynamic Geometry Software edited Construction- {Constructions.ggb} Constructing a Visual Representation of Fractions Using Geog…
    Construction-
    {Constructions.ggb}

    Constructing a Visual Representation of Fractions Using Geogebra-
    This will describe how to create a visual representation of a fraction as parts of a 10x1 rectangle. We will be able to manipulate the sliders to change the
    ...
    2. Create connected 10 horizontal line segments with length 10/a, and a line segment with length 1 at the far left point on the line going vertically. Create another 10 horizontal line segments with length 10/a parallel to the first 10 and connected to the length 1 vertical line. Connect these 2 horizontal lines at each point, creating 10 rectangles with height 1 and 10/a length.
    3. Use the Object Properties to set the first rectangle to only appear when a >= 1, the second to only appear when a >=2, and so on.
    ...
    so on.
    5. Finally, hide all the points and labels on your construction. This will work as a visual representation proper fractions.
    {FractionRepresentation.ggb}
    Discussion questions-
    I chose to do it as a rectangle, because it felt more intuitive to construct to me, and clearly illustrates the fraction. A circle construction would have worked just as well. I set the range of the denominator from 1 to 10 so that I never deal with denominator 0, and the range of the numerator from 0 to a so that improper fractions cannot be created.
    (view changes)
    9:10 am
  3. 9:10 am
  4. page Dynamic Geometry Software edited Constructing a Visual Representation of Fractions Using Geogebra- ... change the 1.Create …
    Constructing a Visual Representation of Fractions Using Geogebra-
    ...
    change the
    1.Create

    1.Create
    2 sliders,
    ...
    b, with a having a range 0of 1 to 10 and an increment of 1, and b having a range of 0 to a with an increment
    ...
    the numerator. leave them both at 10 for the time being.
    2. Create connected 10 horizontal line segments with length 10/a, and a line segment with length 1 at the far left point on the line going vertically. Create another 10 horizontal line segments with length 10/a parallel to the first 10 and connected to the length 1 vertical line. Connect these 2 horizontal lines at each point, creating 10 rectangles with height 1 and 10/a length.
    3. Use the Object Properties to set the first rectangle to only appear when a >= 1, the second to only appear when a >=2, and so on.
    4. Use the polygon tool to create polygons over each of the rectangles. Set these polygons to only appear when b>=1 for the first, b>=2 for the second, and so on.
    5. Finally, hide all the points and labels on your construction. This will work as a visual representation proper fractions.
    Discussion questions-
    I chose to do it as a rectangle, because it felt more intuitive to construct to me, and clearly illustrates the fraction. A circle construction would have worked just as well. I set the range of the denominator from 1 to 10 so that I never deal with denominator 0, and the range of the numerator from 0 to a so that improper fractions cannot be created.

    (view changes)
    9:05 am

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