“The pursuit of truth and beauty is a sphere of activity in which we are permitted to remain children all our lives”
We constructed this spherical pi to commemorate pie. We chose a sphere because while a circle is an elegant shape it just seems so two-dimensional.
March 14th is pi day, the birthday of Einstein, and is also known as being 1 month after Valentine’s Day (for ladies). Therefore in choosing our filling, we decided that stuffing it with steak would be most appropriate, at least according to the internet. Since we currently reside in Quebec we decided to follow flavours akin to a tourtiére. So our pie commemorates pi, the other Valentine’s Day, as well as the local flavours of Quebec & Canada. Ladies take note: the way to a man’s heart is not only though his stomach but also with a juicy... edible math sculpture.
Let’s get started!
Step 1: Follow the Steps
This Instructable is broken down into 4 simple stages:
Step 2: The Filling
Tourtiére is a classic French-Canadian meat pie typically eaten during Christmas time. We chose a Tourtiére du Lac St. Jean style using stout-braised beef shoulder gently spiced with flavours of thyme, cloves, and allspice. Our sphere has a radius of 8 cm (see “The Construction”) therefore it occupies a volume of 2144 cubic cm. Each cubic cm of water = 1 ml. ~250 ml per cup means we need to fill roughly 9 cups of volume with steak. This recipe makes about 10% more than that amount minus what disappears over the course of the procedure as one gets hungry.
2 kg boneless beef shoulder
3 medium onions, diced into 0.5 cm cube
1 large carrot, diced into 0.5 cm cube
4 cloves of garlic, minced
4 starchy potatoes, peeled and chopped to 2 cm cube
1 tsp dried thyme
1 tsp dried rosemary
¼ tsp ground cloves
½ tsp ground allspice
¼ tsp ground cinnamon
2 bay leaves
500 ml stout beer
1 cup homemade beef stock
1 Tb olive oil
Salt and ground black pepper to taste
Preheat oven to 250oF.
Heat oil over medium heat in an oven-proof pot. Rub salt and pepper over the beef shoulder. Add beef to heated pot and brown shoulder on all sides. Once browned, remove beef from pot and set meat aside on a plate.
Step 3: The Filling
To the heated pot now add diced onions, carrots, and garlic. Sweat vegetables until translucent. Around 5 min.
Add thyme, rosemary, cloves, allspice, cinnamon, and bay leaves and stir to combine. Slowly pour in the stout beer to deglaze the pot, scraping up any brown bits using a wooden spoon. Stir in beef stock and bring to a boil.
Step 4: The Filling
Add back the beef and any juices into the braising liquid. Cover and place in the middle of the preheated oven for 2 hr.
After 2 hr, remove the pot from the oven and transfer the meat to a cutting board. Cover the meat in foil and set aside. Add the potatoes, cover pot, and place back into the middle of the oven.
After 30 min, remove the stew from the oven. Roughly chop the beef into 1-2 inch chunks and re-add to the stew. Pick out the bay leaves and discard. Set meat aside and let cool before proceeding to filling.
TIP : The meat can be made 1-2 days prior to assembly of the pie. If doing so, store it in the refrigerator. You can also eat the stew as is; just thicken the braising liquid with a bit of cornstarch and wash it down with a couple of brews for an easy/rustic home-cooked meal sure to impress the missus.
Step 5: The Pastry
For the pastry, we decided to make something with a bit more heft and rigidity to be able to hold the beefy filling. To this end, we constructed a pâte brisée, a typical crust used for quiche Lorraine and other self-standing quiches and tarts. This crust offers a strength advantage from the use of egg yolk and the high fat to flour ratio make it more forgiving than other pie dough.
Ingredients : For a sphere with C = 50 cm (to determine the size of your sphere see “The Construction”)
500 g all purpose flour
250 g butter, chilled and cut into pieces
2 egg yolks (save the whites for later use as an adherent)
3 tsp salt
water as needed
Step 6: The Pastry
Sprinkle the salt into the flour and toss lightly with your hands. Pour the flour into a mound on a clean, dry working area (e.g. wood table). Hollow out the center so it looks like a volcano.
Place the butter in the center of your mound. With your fingers gradually work the flour into the butter until it forms a crumble. Re-form a mound with the butter and flour mixture and once again hollow out the center.
Drop the egg yolk in the middle of the mound and mix in a few drops of water with your finger tips. The amount of water needed will depend on the humidity and the heat of your working environment as well as the warmth of your hands. Continuing to mix with your fingertips, gradually incorporate the flour and butter mixture until you are able to form a ball. With the palm of your hand, push the dough into the table until it achieves a homogenous consistency. It will appear more yellow in color and the dough will become smoother. You may need to add water to help make smoother dough.
Pat the dough into a self containing ball, cover in plastic wrap and chill for at least 30 min.
While the dough is resting you can proceed to “The Construction”.
TIP: The texture of the dough is very important. If it is too dry, it will crack and be difficult to wrap/close around the balloon. If it is too wet, it will slough off the foil as it cooks.
Step 7: The Construction
The best way (seemingly the only way!) we found to assemble this spherical style of pie is to blind bake the pastry crust before filling the pastry with meat. Numerous previous attempts involved frozen beef stew filling, high temperature broiling; even salt-crust baking and each resulted in a sloppy, mushy failure.
The idea behind this method is to sandwich the dough between two supports: a foil scaffold and an oven-safe bowl. Between these two supports, the dough can set so that it won’t get weepy/soggy. A balloon is used to make the foil scaffold, and is fished out through a hole in the pastry before baking. As with any pastry, make sure to keep everything cold, even your hands. My hands: warm because of my big heart. My girlfriend: not so warm.
Egg whites (reserved from pastry making)
Beefy steak meat filling
Preheat oven to 400oF.
Measure the inner radius of your oven-safe bowl. Assume the foil scaffold will be about 0.5 cm in thickness and the pastry will be rolled out to ~0.5 cm thickness and subtract 1 cm from the radius of the bowl. Calculate the circumference (this will be the circumference of the balloon).
Step 8: The Construction
Blow up the balloon. Use a piece of kitchen twine and tape measure to check the circumference.
Step 9: The Construction
When you achieve the circumference that you calculated, wrap the balloon with 4 sheets of tin foil so that the foil reaches, but does not cover, the knot at the top. Construct three 1-inch thick straps by folding sheets of aluminum foil accordion-style. Place these in an asterisk pattern and wrap them around the foiled balloon. These will help hold the foil, maintain the hole, and can act as a handle.
Generously spray the foil scaffold with cooking spray. Also, generously grease the inside of the bowl you will be cooking in.
TIP: If making a design on the sphere with pie crust cut-outs, create the design first and chill them before forming the sphere. This way they will be ready to adhere, using egg white, when the sphere is formed. To make colored pie dough, add food coloring to the liquid of the pie dough before initial mixing.
Step 10: The Construction
To cover the scaffold with the pastry dough, one could simply roll out a big rectangle and drape it over the foil scaffold; cutting excess and patching holes. We thought this to be wasteful so we generated an outline using this online reference: http://www.gma.org/surfing/imaging/globe.html
If you want to be super geekinums you could also calculate out your angles following this guide: http://www.ict.griffith.edu.au/anthony/kites/parafauna/chute_design/
Step 11: The Construction
Roll out the dough to about 0.5 cm thick and make it at least 5 cm longer than the measured circumference of the balloon and 5 cm wider than half the circumference, to ensure a good overlap. Using the outline as a guide, cut out the pie dough and leave about 0.5 cm of wiggle-room around the whole cut-out. Remove the extra dough from the work area and set aside to patch up any holes or for decoration.
Step 12: The Construction
Gently place the dough around the foil scaffold balloon. Fold in the gores of the pastry dough following the contours of the sphere. Seal the seams of the dough using the egg whites, ensuring that there are no cracks or holes through which any liquid can leak. If you want to add any designs to the exterior of the pie then add it now. Place the whole thing into the well-greased oven-safe bowl.
Cut an opening with a diameter of at least 5 cm around the balloon knot. This will become the top of your pie. While holding the knot, pierce the balloon with a needle to deflate and remove it from the scaffold. The foil should be sufficient to support your piecrust in the proper spherical configuration.
Freeze your pie crust for at least an hour and let it rest at room temperature for at least 10 minutes before shoving into the oven.
Place in a preheated oven at 400oF to blind bake for 1 hr or until slightly golden and hard to the touch.
TIP: If the top begins to brown too much, cover it lightly with a piece of foil until the dough finishes cooking.
Step 13: The Construction
Once cooked, carefully remove the sphere from the bowl by tipping it over. Let cool completely. Once cooled, carefully remove the foil scaffold from within the center of the pie. This will require some patience and would benefit from the use of tongs or chopsticks.
As soon as the foil has been completely removed it is time to add the steak filling. Using a large mouth funnel, spoon the braised meat and potatoes into the pie-crust. Use the end of a wooden spoon to carefully push the filling through the funnel and to disperse the stew along the inside of the sphere.
Once the pie crust is stuffed full with meat, cover the top hole with pie dough leaving room for air to escape. Cover the entire sphere in an egg yolk wash and place back in the 400oF preheated oven on a foil ring. Cook for 15 – 20 min or until the pie has a golden brown hue. Remove from the oven and let cool for a bit before cracking it open.
Step 14: The Result
As can be seen from the pictures our pie baked up golden brown, while the insides remained moist and beefy. The pie has a substantial heft; not unexpected since we packed in over 2 kg of delicious, juicy meat. Measurements with kitchen twine showed that it retained a spherical shape along the three major axes, though the bottom was flattened a bit due to the nature of our bowl.
This mathematical specimen of pie greatness is perfect for the romance of pi day and is best enjoyed warm with a full-bodied red wine and a beautiful lady sitting across a candle-lit table. Of course, if this isn’t the case (and seriously, how can someone that celebrates pi day with such devotion NOT have a beautiful lady date?) this pie is still perfect for the occasion, with the right injection of creativity (Fig. 3).
We hope you found this Instructable informative, educational, and entertaining.
Best of luck in your future pi endeavors!
Runner Up in the
Serious Eats Pi Day Pie Contest