Ancient Knot

As a math teacher, I am always looking for something interesting for my students to do in class.  I came across the following resource. 
http://www.math.nmsu.edu/breakingaway/Lessons/ancientknot1/ancientknot.html

I am intrigued by this ancient knot and I am happy to find this design has roots in mathematics. I used their instructions and created the following ancient knot.

 Ancient Knot Design on a 12 x 12 piece of paper

 I have seen this same design at the Textile Museum in Washington, DC in Kuba textiles at the Woven Art of Central Africa exhibit in 2011.  The Africans used different color plant materials to create their designs. The plant material was worked to the point that the fibers softened and they were amazingly able to create velvet. 

I think this design would look beautiful in a quilt because as the math blog says,

 "It has no beginning or end, and according to folklore, it represents longevity and immortality."

What a beautiful thing to put into a quilt which is a labor of love.  You could use the Silhouette fabric blade to cut out all of the pieces which would simplify cutting the intricate pieces.

Here is the PDF of the knot.
https://drive.google.com/file/d/0B7oGIyVDbRGYbEhfRFlKcG16Mnc/view?usp=sharing&resourcekey=0-CCL6EOZgsPGTQAh0EvT8EA

Here is the .Studio file of the knot.
https://drive.google.com/file/d/0B7oGIyVDbRGYTGdic0RjUVhRcHM/view?usp=sharing&resourcekey=0-2GfF9NuF8LWHs-7p0hBEVQ

Holly Wreath Torus

 Holly Wreath Torus

 

Side view of the torus...notice the swirling pattern...lovely!

I love the torus shape.  It is a sliceform that swirls around and is fascinating to look at.  I modified my original torus and created this holly wreath design.  This torus shape has been discovered by a fellow papercrafter, Carol at http://extremecards.blogspot.com/2013/11/preview-holly-wreath.html from my blog.  She created a leaf torus and then created a holly wreath torus.  She posted her holly wreath torus a few weeks ago.  I think her holly leaf design is a little bit more shapely than mine but the holly leaf shape is still the same...great minds think alike!  Please note...I did not copy her.  I have had this design for quite a while and I just didn't have the time to publish it...too many designs and not enough time as my sleep can attest to.

 

Here is the PDF file of the holly leaf torus and the bow.
https://drive.google.com/file/d/0B7oGIyVDbRGYU3dOMXJqVnQyZTQ/view?usp=sharing&resourcekey=0-_VCyTl1hdFZPVyzoczKY8w

The bow is not the same exact size as the one in the photograph and there is one extra ribbon...I decided I wanted a little more intricate design for the Bow ornament.  The Silhouette software had an error and the original design was lost in restarting the program...back to square one.  Oh well..lessoned learned...always save your design...software errors abound! However, something good came out of it, I created another ornament which I would not have done originally.

Here is the .Studio file for the holly leaf torus and the bow.  I used cardstock.
https://drive.google.com/file/d/0B7oGIyVDbRGYc2tTU3I0d1lFMU0/view?usp=sharing&resourcekey=0-jl2F5G1phcMYlPgF0Un77w


To make the holly leaf torus, there are two pages of toruses.  One page has the slit on top and the other has the slit on the bottom.  Always start in the middle and end in the middle.  It makes everything easier.  Be very slow and methodical when doing this torus.  The points of the holly like to get stuck to one another but everything works nicely if you are patient.  If you ever get frustrated, just walk away and take a breather. It will be very satisfying when it is completed.  The directions for the torus are on a previous post. http://papercraftetc.blogspot.com/2013/10/a-honeycomb-pumpkin-decoration-for-fall.html

To make the bow.  Curl the bow tie piece into an oval as shown below.

 Put a dab of glue under the bow tie.

 

 Put glue on the rectangular piece which wraps around the bow tie.

 Put glue on the bow tie and ribbon pieces and attach to the back of the bow.

 I added a square piece of paper to the hangar (not given...just cut a little square with scissors) to give the bow more strength as an bow ornament.  This does not need to be done if you are making the holly wreath torus.
 

 

Bow Ornament

 

 

I added a string to the Holly wreath so that I could hang it on the Christmas tree.

 

 

Merry Christmas!

 

 

#torus #Christmas Ornament

The Perfect Desktop Christmas Tree

This Christmas tree has all the elements of a big tree but in a desktop version.  I love the paper doll garland and the gold spiral garland.  The ornaments can be resized for your room size tree.

The Christmas tree is assembled by sliding the pieces together.  Two of the pieces are exactly the same.  Spread them apart and place them in the base so that the are all equally spaced.  This is  similar to the witch's hat base in another post.  http://papercraftetc.blogspot.com/2013/10/halloween-witchs-or-wizards-hats.html 

Here is the PDF of the Christmas tree.
https://drive.google.com/file/d/0B7oGIyVDbRGYTUIzNmQweTJNZlU/view?usp=sharing&resourcekey=0-soe-zCEL-XLgwQrZAy_wJw

Here is the .Studio file.  I used cardstock on the tree and ornaments.  The spiral gold garland and the star on top of the tree is good quality wrapping paper.  The paper doll garland is white copy paper.
https://drive.google.com/file/d/0B7oGIyVDbRGYZ1AxMjQ0SldVNms/view?usp=sharing&resourcekey=0-sE7l-4SZK-7upUg1keduOg

 

 

 

Merry Christmas!

Peace Dove Ornament

 

 Desk model of peace dove ornament

 

I love this ornament.  The dove is so pretty with the olive branch in its mouth.

Here is the PDF of the dove.  There are three versions...two desktop models and a hanging ornament.
https://drive.google.com/file/d/0B7oGIyVDbRGYOHlfOU9tR3FLQ1E/view?usp=sharing&resourcekey=0-k0hRQmcvY2GZ_Hl8qsi67g

Here is .Studio file.  I used cardstock.  There is a shim piece to place in the center of the wing so that there is no movement after gluing.
https://drive.google.com/file/d/0B7oGIyVDbRGYZkEtTFhPR1UxbXM/view?usp=sharing&resourcekey=0-lTg4GTVdXJouiCzwK-FeNg

There is a fourth version here.  I eliminated the olive branch in one of the hanging ornaments.

Star of David Spinner

I created two versions of this star.  One is a hanging ornament and the other is a desk model.

 Here is the PDF.  It is not a very good PDF as it does not show the lines correctly.  All of the lines are connected except for the center points have a small gap.  This small gap is where the paper is  attached as a whole which allows for the spin to occur.
https://drive.google.com/file/d/0B7oGIyVDbRGYMjdtZm8xdHd4eUE/view?usp=sharing&resourcekey=0-SIQ2MHVr_8BZI18YpVfGXw

Here is the .Studio file. I used cardstock.  Assemble the star as shown in the picture below. Each star goes in the opposite direction to create the spinning effect.
https://drive.google.com/file/d/0B7oGIyVDbRGYRHZlV3IySWRyRUE/view?usp=sharing&resourcekey=0-wcl8UD3zxA60P37aRfN0hw

Happy Hanukkah to all my Jewish friends!

P.S.  Check back later as I have quite a few more spinners to post but not enough time.

How can you make a cone with analytical geometry? Or Pretty Cone Trees!

Cone Sliceform from derived equation

 

  

My husband wrote this blog post  with the mathematical analysis and now I am updating it with the PDF's and .Studio files.  Let me explain...my husband is taking an analytical geometry course and he gave me the graphs to create this cone. I think he did a fabulous job!
 

 I love the reflection of the trees in the glossy surface.

 





I think the cones look terrific as trees with my paper house from a previous post. http://papercraftetc.blogspot.com/2013/09/i-love-making-houses.html Don't you agree?

 

Using the distance formula r^2 = sqrt(x^2+y^2) and the formula for the line in x-z space z=h/a(x) and knowing that the radius r must equal the x value in x-z space, you combine both equations.  This gives you the equation for the surface z = h/a(sqrt(x^2+y^2).  You can change the height to radius using the parameters h and a. 

To create the sliceform, you need three slices in each direction.  Using the golden ratio height/base = 1.6, so height/radius = 3.2. Next, find equations for each slice in z-y space by setting x.  For a six inch height, radius = 6/3.2 = 1.875.  Divide this into four increments of 0.469 inches each to set x.  This gives these four equations in z-y space:



For x=0:           z=3.2sqrt(y^2)

For x=0.469:    z=3.2sqrt(0.469^2+y^2)

For x=0.938:    z=3.2sqrt(0.938^2+y^2)

For x=1.406:    z=3.2sqrt(1.406^2+y^2)

 

The PDF and .Studio files were created for just one of the trees.  The files will need to be resized if you would like to create a forest of trees like I did in the pictures above.

 

Here is the PDF of the cone sliceform.

https://drive.google.com/file/d/0B7oGIyVDbRGYMS1DNFJ3aEF3OXc/view?usp=sharing&resourcekey=0-ZBqVE4e0j2YO3bChQDb2zg

 

Here is the .Studio file of the cone sliceform.  I used cardstock.

https://drive.google.com/file/d/0B7oGIyVDbRGYZ3hXZTRkSkJ1Wm8/view?usp=sharing&resourcekey=0-k8y_018m71wMin7K0uhTFw

 

 



Planning a Holiday Meal Project

 

 

I love to apply math to real life situations. I created the following math project for my fourth grade students. I have included all materials necessary to implement this project in the following PDF except for the grocery advertisements. (This information is also available online because most grocery stores post their advertisements online).  I also created a .Studio file of a turkey silhouette.  I cut out one turkey per student for their project.

Here is the PDF files for the math project.
https://drive.google.com/file/d/0B7oGIyVDbRGYWG5tMjFIeFVVdGs/view?usp=sharing&resourcekey=0-yGbedgeC8xpIm2g6ixfx3Q

Here is the PDF file for the silhouette turkey. 
https://drive.google.com/file/d/0B7oGIyVDbRGYMWxOb05UM3NGQTg/view?usp=sharing&resourcekey=0-Tmp8K7sZtdVHY0av6_qB7w

Here is the .Studio file for the silhouette turkey.
https://drive.google.com/file/d/0B7oGIyVDbRGYczluYkNxdXdUUjg/view?usp=sharing&resourcekey=0-CAoakyIPaMsrwLXTnk63rw

Planning a Holiday Meal

 

Thanksgiving dinner will be served at your home this year for ten people.  Using the local supermarket advertisements, plan the meal’s cost using the following menu and serving recommendations. Calculate the quantity needed.  Remember you need to round up to the next amount since you need enough food for everyone.  Calculate the cost of each item by multiplying the quantity by the cost. Do all of your calculations in the space provided and circle your answer.

Serving recommendations:

— Turkey:  1 pound per person
— Gravy:  3 oz. per person 
— Stuffing:  1 oz. per person 
— Green Beans:  3 oz. per person
— Potatoes:  1/2 lb. per person 
— Corn:  3 oz. per person 
— Rolls:  1 per person 
— Butter:  1 tsp. per person   (96 tsp. in 1 lb. of butter)
— Cranberry sauce:  14 oz. can has 5 servings 
— Pumpkin Pie:  a 9-inch pie can be cut into 8 slices 


Transfer your quantity and cost calculations to the “Planning a Holiday Dinner” table.

Calculate the total cost of the meal by adding up all of the items to be purchased in the “Planning a Holiday Dinner” table.  Write the total cost in the table.

Write a check for the total cost of the meal.

Cut out a picture of each item, if available, with the price from your grocery advertisement.  Using a piece of construction paper, decorate your project with these pictures. Cut out the check and attach it your project along with the “Planning a Holiday Dinner” table. You may create this project in a book format or as a poster. When writing the check, the dollar amount is in word form, the cents are written as a number of cents over a hundred.  For example. $135.45, is written as One Hundred Thirty Five 45/100 with a line going through the rest of the space. 

 
 Happy Thanksgiving!

 

  
 

Thanksgiving Headdresses

Headdresses made by students

I remember as a child in first grade making Thanksgiving headdresses.  I made a few versions. I have made two types of turkeys with different feathers, a pilgrim hat, and an Indian headdress.

Here is the .Studio file. I used cardstock.

https://drive.google.com/file/d/0B7oGIyVDbRGYWF9tVF8wV1FOTlU/view?usp=sharing&resourcekey=0-S-W2gu5Ht4mZLuPTy3UqtA

Here is the .PDF file.

https://drive.google.com/file/d/0B7oGIyVDbRGYYlpiSF9JLVpJYkU/view?usp=sharing&resourcekey=0-RbP9lAEnzcihjD3j6Z3Y9g

Slide buckle through the smaller band and attach to the larger band

I used a glue stick to glue the buckle on.  Bend the paper a little to conform

to the curvature of your head.

I used a glue stick to glue all of the parts.  It makes the paper

pliable so that you can bend it a little.

The little turkey on the Happy Thanksgiving headband is 3D. 

The head protrudes a little. There are perforations to where it bends. The different colors were made by cutting different feathers and interchanging the parts.

I added feathers to the Indian headdress.

 

 I used the decorations as a Thanksgiving window dressing at school.

 

 



Who Plucked The Turkey?

This post is just a reflection...no instructions included for the turkey...see the previous post "Plucking Turkey Feathers" for directions.

I have two very mischievous kitties, Marley and Melvin and they both love paper.  I generate a lot of paper scraps in designing my paper models.   Instead of throwing the scraps away, I put them on the floor and scatter it in a pile so that I can see all of the pieces of paper that could possibly be reused. Yesterday, Marley came into the craft room crying that he was bored, he took one look at the pile of paper, kicked a few around and found the perfect victim, a round disc with a hole cut out in the middle. It fit perfectly in his mouth and he ran happily out of the room and down the stairs yowling all the way.  Marley dropped the paper eventually when he was done. Melvin came along and finished the job of destroying the enemy.  He chewed on it until it didn't look like its former self.

Today, I walked into the kitchen and there on the floor was my turkey decoration with a turkey feather sitting a few feet away.  "Who plucked the turkey?", I said out loud and two kitties came running.

"Who plucked the turkey?"

Melvin says "What is this on the floor?"

Marley says, "It wasn't me...I'm innocent...look how pretty I look."

Melvin says, "Hmmm...this smells pretty good."

Melvin says, "Yup, this is really tasty!"

Love this animation of what actually happened.

Plucking Turkey Feathers



This table decoration can pull double duty.  It is beautiful to look at but it can also be a trivia game...that is why I entitled this post, "Plucking Turkey Feathers".  There are 45 feathers and you can put interesting Thanksgiving trivia questions on them.  The person who guesses the most questions wins another slice of pie for Thanksgiving dinner. Or for those math teachers out there.  You can put 45 math problems on them and let the student select which one they want to do....just write numbers on the feathers and put them randomly in the plume. Have a sheet of 45 math problems and give the students the corresponding question.  You can reuse the turkey for different classes by reinserting the feathers.

Here is the .Studio file for the turkey.
https://drive.google.com/file/d/0B7oGIyVDbRGYMFpjeXpVODJTSnc/view?usp=sharing&resourcekey=0-bvd5eSAJHMHrbLOpDHVxTw

Here is the PDF of this same turkey if you do not have a Silhouette.  There is a lot of cutting by hand but I think it is definitely worth the effort.
https://drive.google.com/file/d/0B7oGIyVDbRGYR3ZEZkd4WTZtd1k/view?usp=sharing&resourcekey=0-M46bTnmL_KeLfbZ8CTSsWQ

 

Cut out the base out of chipboard or a cereal box. Cut out another base this time out of decorative paper.  Glue the decorative paper to the chipboard...make sure that you align the slots.  One of the slots is smaller than the others.  This smallest slot is where the turkey body gets attached.

 

 

Can you guess how I made the shape of the turkey body?

Decorate the turkey body with the eyes, beak, hat and waddle before you glue the body to the base.  I made two copies of the hat and brim so that the turkey will look nice on both sides. Also attach the honeycomb decoration, if you would like but it is not necessary.  This honeycomb is created using a torus villarceau circle.  I mentioned its origin in a previous post. http://papercraftetc.blogspot.com/2013/07/sliceforms-are-my-new-obsession.html

The directions for making it are on the pumpkin post.
http://papercraftetc.blogspot.com/2013/10/a-honeycomb-pumpkin-decoration-for-fall.html

The turkey body is in the shape of a bowling pin!

 



Cut out 9 copies of each semicircle to make the honeycomb.  Glue it to the body as shown below. Cut out another turkey body and glue it on the back before you attach the hat.  I forgot and had to slide the turkey body under the hat.  I also add a spine to the center of the body as shown in the picture to give the turkey more support (I cut this out of the chipboard with scissors as there is no need for a perfect measurement.) Here is the back of the turkey.

 

Spine is the gray piece of paper

 



I glued the feet together and have them facing forward.  The tabs will be split apart.  One will be glued forward and the other backward on the bottom of the chipboard base. You will have to cut the backward facing tab a little...1/8 of an inch since I did not want to make the front facing tab any smaller.  Glue the feet to the base.

There are three sizes of feathers and corresponding fan bases.  You need to cut out 15 feathers and two fan bases for each set of feather plumes.

Glue the two fans together but do not glue the tabs together.  These tabs will be used to adhere the fan to the base. Insert the tabs in the base.  Rip off the side that will interfere with the next base.

 Repeat for the other two fan bases.  Slide the feathers into the fan base. I liked inserting the smallest, then the middle and then the largest feather...continuing through the entire fan.

 

Two fans attached...one more needs to be added.

 

 

 

 

Attaching the feathers from one side to the other.



 

The back side of the turkey looks just as beautiful as the front.



Mayflower Thanksgiving Decoration

Using the same body from my Columbus ship,  I recreated a model of the Mayflower.  The Mayflower is flying the St. George's Cross. St. George was the patron saint of England.  I learned on our recent trip to England that the current English flag, the Union Jack is a mixture of the flags of England, Scotland and Ireland.

Here is the .Studio file for the Mayflower.  I used cardstock.
https://drive.google.com/file/d/0B7oGIyVDbRGYakxiR2lNYzBydzQ/view?usp=sharing&resourcekey=0-RHk5jG852lU6YcKVE2QoPg

Here is the PDF.
https://drive.google.com/file/d/1SsAecOexDsoC2DmNfZnQs2B_P-PFAXYG/view?usp=sharing

Please view my previous post as to how to put the ship together as the directions are the same except for the pole in the front of the ship which I glued directly to the front mast pole and the flag.  I cut a vertical 1 inch slit in the mast pole starting at the top and glued the flag to the pole as shown in picture.

My previous ship post:
http://papercraftetc.blogspot.com/2013/10/can-you-name-three-ships-that-sailed.html