Deprecated: Creation of dynamic property wpdb::$categories is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 668

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Deprecated: Return type of WP_Theme::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 554

Deprecated: Return type of WP_Theme::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 595

Deprecated: Return type of WP_Theme::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 535

Deprecated: Return type of WP_Theme::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 544

Deprecated: Return type of WP_REST_Request::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 960

Deprecated: Return type of WP_REST_Request::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 980

Deprecated: Return type of WP_REST_Request::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 992

Deprecated: Return type of WP_REST_Request::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 1003

Deprecated: Return type of WP_Block_List::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 151

Deprecated: Return type of WP_Block_List::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 175

Deprecated: Return type of WP_Block_List::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 164

Deprecated: Return type of WP_Block_List::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 186

Deprecated: Return type of WP_Block_List::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 138

Deprecated: Return type of WP_Block_List::offsetExists($index) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 75

Deprecated: Return type of WP_Block_List::offsetGet($index) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 89

Deprecated: Return type of WP_Block_List::offsetSet($index, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 110

Deprecated: Return type of WP_Block_List::offsetUnset($index) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 127

Deprecated: Return type of WP_Block_List::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 199

Deprecated: Creation of dynamic property Automattic\Jetpack\Connection\Manager::$error_handler is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-connection/src/class-manager.php on line 91

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Instagram_Gallery::$is_wpcom is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-instagram-gallery.php on line 23

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Mailchimp::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-mailchimp.php on line 17

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Tweetstorm_Gather::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-tweetstorm-gather.php on line 21

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Tweetstorm_Gather::$is_wpcom is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-tweetstorm-gather.php on line 22

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Gutenberg_Available_Extensions::$wpcom_is_site_specific_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/gutenberg-available-extensions.php on line 20

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Memberships::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/memberships.php on line 23

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Memberships::$wpcom_is_site_specific_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/memberships.php on line 24

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Subscribers::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/subscribers.php on line 15

Deprecated: Creation of dynamic property Automattic\Jetpack\Sync\Queue::$random_int is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-sync/src/class-queue.php on line 38

Deprecated: Creation of dynamic property Automattic\Jetpack\Sync\Queue::$random_int is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-sync/src/class-queue.php on line 38

Deprecated: Creation of dynamic property WPCOM_Widget_Goodreads::$shelves is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/modules/widgets/goodreads.php on line 33

Deprecated: DateTime::__construct(): Passing null to parameter #1 ($datetime) of type string is deprecated in /var/www/twodee/blog/wp-includes/script-loader.php on line 348

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$toolbar_classic_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 347

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$toolbar_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 349

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Deprecated: Creation of dynamic property Advanced_Editor_Tools::$panels_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 351

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$used_block_buttons is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 354

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: ltrim(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 3030

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

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Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

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Deprecated: Creation of dynamic property WP_Term::$cat_name is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 381

Deprecated: Creation of dynamic property WP_Term::$category_nicename is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 382

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Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

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Deprecated: Creation of dynamic property WP_Term::$category_nicename is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 382

Deprecated: Creation of dynamic property WP_Term::$category_parent is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 383

Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

Deprecated: Creation of dynamic property WP_Term::$category_description is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 380

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» public

teaching machines

Block vs. Inline-block vs. Inline

If I were to rank the most important things about making a website, I’d write down the following: The content The display property Everything else The display property dictates how the content appears in relation to other content, and it silently cancels out other properties that don’t make sense for one its settings. I find […]

Bathroom Angles

Our bathroom gave me a math problem, and I failed. Herein I document my failure and visualize the answer I should have provided. When we bought our home, the bathroom had carpet but no baseboard. This combination makes painting the walls difficult. As we are preparing to paint, I decided to install some baseboard. Measuring, […]

Coscars

Something came in the mail this week from the University of Canterbury in New Zealand. The Department of Computer Science and Software Engineering (who use COSC as a prefix for their computer science courses) just held their end-of-year awards ceremony, the COSCARs. I was honored with this Most Wholesome Lecturer award: How exactly I was […]

Cutting Corners

I learned recently of Chaikin’s Algorithm, a method for rounding off the corners of a polygon. The algorithm works like this: Find the midpoints of each line segment in the polygon’s perimeter. Connect each consecutive pair of midpoints using a quadratic Bezier curve. The midpoints are the curve’s endpoints. The vertex between them is the […]

Circle Dance

At one time, people believed that the Earth was the center of the universe, and that the planets and the sun orbited around it. Copernicus came along and challenged this idea, suggesting that the sun was the center. These are the only two sides of the debate that we ever hear about. Heliocentrism vs. geocentrism […]

Background Check

There’s somebody on Twitter named Dave who makes animations that break your mind. I fell in love with a simple rotating one a couple of weeks ago and recreated it in Twoville: Several others have recreated it too, but they appear to have fallen for the same trap that I initially fell for. They enumerated […]

Progress in Twoville

Today was a non-teaching day, so I made some “progress” in Twoville: You could summarize my professional career as one long effort to get to the point where I can express non-trivial ideas about shapes and animations in around 30 lines of code that doesn’t need to be compiled.

Triangular Colors

Last week I was trying to think of boolean predicates that I could use for exercises in an introductory programming class. I remembered the triangle inequality, which states how the lengths of three line segments must relate if they are to be formed into a triangle. In short, each segment must be shorter than the […]

Power Set of Venn Diagrams

In our introductory programming class, I try to reframe abstract logic into concrete spatial thinking. One way I do this is through the game Trux Falsy. Another way is through Venn diagrams. I want students to see how the AND operator creates an intersection, how the OR operator creates a union, and how DeMorgan’s Law […]

Terra’s Theme

I’m not exactly sure what Deltaphone is for, but this afternoon, it was for analyzing the structure of Terra’s Theme from Final Fantasy VI. (Thanks to 8-bit of 8-bit Music Theory, who did all the work.) The melodic line consists of a phrase repeated three times, and this phrase is expressed in the prefix function […]

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